Zhen WangpersName, Marko JusuppersName, Lei ShipersName, Joung-Hun LeepersName, Yoh IwasapersName, Stefano BoccalettipersName (2018date). “Exploiting a cognitive bias promotes cooperation in social dilemma experiments.” Nature Communicationstitle·j.
Object of study — whether adding an inferior rewardterm option changes cooperationterm in a repeated prisoner's dilemma
Research question — whether a decoy can induce an initial burst of cooperationterm and whether reciprocal play stabilizes it
Contribution — experimental evidence that choice architecture can exploit the decoy effectterm to elicit durable prosocial actionterm·var
phenomenon · claim-type · cross-domain-transfer · mechanism · claim-relation · replication-status · limitation — grounded in the full text| phenomenon | an inferior, rarely chosen reward option substantially increasing cooperation — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” | |
| claim-type | mechanism — “Returning to the question on the mechanisms underlying selection, we attempt to provide an answer by connecting several pieces of evidence. First, the results here, as well as that of a similarly structured experiment 32 , were successfully recreated in computer simulations using the data on how opponents respond to each other’s most recent actions (Supplementary Note 4 ; Supplementary Fig. 6 ). That most recent actions are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 3 . To the extent that noise cancels out, which is a first-order effect, TFT should propagate initial frequencies of cooperation C and defection D through time because C is met with C and D is met with D . We find, however, that noise fails to cancel out completely, but rather exhibits a second-order effect in the form of a bias toward defection (Supplementary Note 5 ; Supplementary Fig. 7 ). This second-order effect acts as if the decoy’s effectiveness wears off through the course of an encounter. Fortunately, at the beginning of the very next encounter, the decoy’s effectiveness is restored, causing volunteers to be more cooperative again. The overall result is that, despite the fact that volunteers correctly perceive reward R as an inferior option, the initial burst of cooperativeness caused by the decoy effect is stabilised across more than 80 rounds of the game (Fig. 2 ).” | |
| method — evidence | — “We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatment, wherein the only actions available were cooperation ( C ) and defection ( D ), with a decoy treatment, wherein an additional action to “reward” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices:” | |
| object of study — evidence | — “The decoy effect is a cognitive bias documented in behavioural economics by which the presence of a third, (partly) inferior choice causes a significant shift in people’s preference for other items. Here, we performed an experiment with human volunteers who played a variant of the repeated prisoner’s dilemma game in which the standard options of “cooperate” and “defect” are supplemented with a new, decoy option, “reward”. We show that although volunteers rarely chose the decoy option, its availability sparks a significant increase in overall cooperativeness and improves the likelihood of success for cooperative individuals in this game. The presence of the decoy increased willingness of volunteers to cooperate in the first step of each game, leading to subsequent propagation of such willingness by (noisy) tit-for-tat. Our study thus points to decoys as a means to elicit voluntary prosocial action across a spectrum of collective endeavours.” | |
| research question — evidence | — “We set up an experimental attempt within the bounds of evolutionary game theory designed to observe the decoy effect at work. Specifically, we organised a repeated Prisoner’s Dilemma (rPD) game which, based on both theory and previous experience 32 , should cause defection to considerably exceed cooperation. We then enriched this game with a third, decoy option to “throw off” players and get them to cooperate with one another early in the game. Finally, we asked whether such an initial burst of cooperation can be stabilised or whether players recognise that from a purely rational perspective the decoy option is irrelevant, leading to a gradual replacement of cooperation with mutual defection.” | |
| contribution — evidence | — “Our study thus points to decoys as a means to elicit voluntary prosocial action across a spectrum of collective endeavours. A hypothetical example would be a small business team in which a member has fallen behind schedule. Although others may be reluctant to put extra hours to help their distressed colleague even if there is adequate overtime pay (the cooperative option), preferences may change by setting this overtime pay to decrease considerably some weeks before the deadline (the decoy option). Explained from such a psychological perspective, our results run the risk of appearing somewhat unsurprising. We therefore invite readers to contrast this explanation with an attempt at explaining why reward is a cooperation promoter solely within the bounds of evolutionary game theory. The latter explanation is unlikely to invoke cognitive biases as particularly relevant and would struggle with reward’s effectiveness before anyone can actually reward anyone. Deeper implications of the results for the evolution of human cooperation are admittedly less obvious (Supplementary Discussion), but with promising research directions crystallised, we believe that maintaining an optimistic perspective is warranted.” | |
| mechanism | An inferior cooperative option increases the relative attractiveness of ordinary cooperation. — “To apply the concept of dilemma strength for our purpose, we recognise from Eq. ( 1 ) that R is another form of cooperation, more costly than C , but also more beneficial for the opponent, and we look at which of the two actions better protects cooperators from excessive exploitation by defectors. Rationality dictates ignoring the form of cooperation that offers less protection, meaning that rational opponents should end up playing a 2 × 2 game consisting of either the ( C , D ) pair or the ( D , R ) pair. We find from Eq. ( 1 ) that for these pairs DS = 2 and DS = 3, respectively. A higher value of DS for pair ( D , R ) points to a less favourable dilemma and forces a conclusion that R is inferior to C . We thus learn that C and R share the defining characteristic of being cooperative actions, but R is inferior to C in another defining characteristic, i.e., resilience to exploitation by defectors. In the context of evolutionary game theory, therefore, R as defined in Eq. ( 1 ) is a valid decoy for C .” | mechanisms[0] |
| mechanism | The decoy shifts first-round choices before direct reward experience is possible. — “Searching for mechanisms that explain improved cooperativeness in the decoy treatment, we find that reward is an effective cooperation promoter even before it can be used. Compared to the control treatment, the odds of an encounter starting with cooperation C (defection D ) are significantly improved (suppressed) (Fig. 3a ). Past the first round, response to C ( D ) in the previous round is overwhelmingly C ( D ) irrespective of the treatment (Fig. 3b, c ). Reward R is mostly met with C or an occasional R (Fig. 3d ). These results suggest that volunteers in our experiment play what can be characterised as noisy tit-for-tat (TFT) (Fig. 4 ).” | mechanisms[1] |
| mechanism | Conditional reciprocity propagates the altered initial cooperation level through later rounds. — “Tit-for-tat (i.e., conditional cooperation) is the prevailing strategy. a To calculate the fraction of tit-for-tat (TFT) actions, we looked at each encounter individually and added all instances in which C was followed by C , D by D , or—when available— R by R (solid lines). This sum was then divided by the total number of possible TFT actions (solid and dashed lines), which equals 2× (number of rounds −1). In the present example, the fraction of TFT actions is 4 5 = 0.8 . b The average fraction of TFT actions in the control treatment is high from the beginning and slowly increases over the course of 20+ encounters (intercept 0.711, 95% confidence interval [0.681–0.742]; slope 0.007, 95% confidence interval [0.004–0.009]; coefficient of determination R 2 = 0.292). Also shown is a breakdown of how much C and D contribute to the total fraction of TFT actions. c The average fraction of TFT actions in decoy and control treatments is similar (intercept 0.715, 95% confidence interval [0.694–0.735]; slope 0.007, 95% confidence interval [0.005–0.009]; coefficient of determination R 2 = 0.485). In the decoy treatment, however, the contribution of cooperative TFT actions is considerably higher than in the control treatment. Reward R contributes very little. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals” | mechanisms[2] |
| mechanism | Renewed pairing restores the decoy effect after within-encounter defection bias accumulates. — “Returning to the question on the mechanisms underlying selection, we attempt to provide an answer by connecting several pieces of evidence. First, the results here, as well as that of a similarly structured experiment 32 , were successfully recreated in computer simulations using the data on how opponents respond to each other’s most recent actions (Supplementary Note 4 ; Supplementary Fig. 6 ). That most recent actions are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 3 . To the extent that noise cancels out, which is a first-order effect, TFT should propagate initial frequencies of cooperation C and defection D through time because C is met with C and D is met with D . We find, however, that noise fails to cancel out completely, but rather exhibits a second-order effect in the form of a bias toward defection (Supplementary Note 5 ; Supplementary Fig. 7 ). This second-order effect acts as if the decoy’s effectiveness wears off through the course of an encounter. Fortunately, at the beginning of the very next encounter, the decoy’s effectiveness is restored, causing volunteers to be more cooperative again. The overall result is that, despite the fact that volunteers correctly perceive reward R as an inferior option, the initial burst of cooperativeness caused by the decoy effect is stabilised across more than 80 rounds of the game (Fig. 2 ).” | mechanisms[3] |
| sense | bias as a predictable context-induced departure from utility-maximizing choice — “Neoclassical economics has ascribed human actions to a relentless rational drive to maximise the (expected) utility 1 – 5 , even as the economic models struggled to account for the full range of displayed behaviours 6 – 8 . The apparent discrepancy between theory and reality ultimately gave birth to the field of behavioural economics, which has since amassed indisputable evidence to the effect that various cognitive biases stand in the way of the completely rational behaviour of economic agents 9 – 12 . Our focus is on the decoy effect, also known as the asymmetric dominance effect 13 or the attraction effect 14 , which appears in multiple-choice situations in which a particular choice called “decoy” shares some defining characteristics with another choice called “target”, but is inferior to the target in one defining characteristic 15 . Because we apply the concept of decoy in the novel context of evolutionary game theory, it is crucial to establish which defining (shared and inferior) characteristics are relevant to this context, as will be done in a moment. We emphasise for now that while decoys should be inconsequential to decision-making, they have been found to increase the attractiveness of the target, even in real-world political elections 16 . The effect’s strength, however, seems to diminish in the presence of more meaningful stimulus descriptions 17 . Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effect 18 – 21 .” | senses[0] |
| sense | reward as a costly prosocial action and an asymmetrically dominated decoy — “In particular, action 1 (i.e., C ) meant giving up one unit for the opponent to receive two units. Action 2 (i.e., D ) meant earning one unit at the opponent’s expense of one unit. Finally, action 3 (i.e., R ) was qualitatively the same as action 1 with the distinction that one would give up two units for the opponent to receive three units in return. Further details on the experimental methods are given in the Methods section and the Supplementary Methods (see also Supplementary Figs. 1 – 3 and Supplementary Table 1). A picture emerging from this experimental setup is that reward is effective in promoting cooperation, but this effectiveness is a consequence of a cognitive bias known as the decoy effect. We therefore conclude that decoys possess an untapped potential to elicit voluntary prosocial action.” | senses[1] |
| sense | control as alteration of a choice set rather than direct compulsion — “Our study thus points to decoys as a means to elicit voluntary prosocial action across a spectrum of collective endeavours. A hypothetical example would be a small business team in which a member has fallen behind schedule. Although others may be reluctant to put extra hours to help their distressed colleague even if there is adequate overtime pay (the cooperative option), preferences may change by setting this overtime pay to decrease considerably some weeks before the deadline (the decoy option). Explained from such a psychological perspective, our results run the risk of appearing somewhat unsurprising. We therefore invite readers to contrast this explanation with an attempt at explaining why reward is a cooperation promoter solely within the bounds of evolutionary game theory. The latter explanation is unlikely to invoke cognitive biases as particularly relevant and would struggle with reward’s effectiveness before anyone can actually reward anyone. Deeper implications of the results for the evolution of human cooperation are admittedly less obvious (Supplementary Discussion), but with promising research directions crystallised, we believe that maintaining an optimistic perspective is warranted.” | senses[2] |
| sense | prediction as game-theoretic expectation about rational action and strategy stability — “We set up an experimental attempt within the bounds of evolutionary game theory designed to observe the decoy effect at work. Specifically, we organised a repeated Prisoner’s Dilemma (rPD) game which, based on both theory and previous experience 32 , should cause defection to considerably exceed cooperation. We then enriched this game with a third, decoy option to “throw off” players and get them to cooperate with one another early in the game. Finally, we asked whether such an initial burst of cooperation can be stabilised or whether players recognise that from a purely rational perspective the decoy option is irrelevant, leading to a gradual replacement of cooperation with mutual defection.” | senses[3] |
| sense | agency as situated choice by economic actors whose preferences depend on available alternatives — “Neoclassical economics has ascribed human actions to a relentless rational drive to maximise the (expected) utility 1 – 5 , even as the economic models struggled to account for the full range of displayed behaviours 6 – 8 . The apparent discrepancy between theory and reality ultimately gave birth to the field of behavioural economics, which has since amassed indisputable evidence to the effect that various cognitive biases stand in the way of the completely rational behaviour of economic agents 9 – 12 . Our focus is on the decoy effect, also known as the asymmetric dominance effect 13 or the attraction effect 14 , which appears in multiple-choice situations in which a particular choice called “decoy” shares some defining characteristics with another choice called “target”, but is inferior to the target in one defining characteristic 15 . Because we apply the concept of decoy in the novel context of evolutionary game theory, it is crucial to establish which defining (shared and inferior) characteristics are relevant to this context, as will be done in a moment. We emphasise for now that while decoys should be inconsequential to decision-making, they have been found to increase the attractiveness of the target, even in real-world political elections 16 . The effect’s strength, however, seems to diminish in the presence of more meaningful stimulus descriptions 17 . Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effect 18 – 21 .” | senses[4] |
| sense | selection as learned elimination of lower-fitness behavior — “Apart from behavioural economics, evolutionary game theory is another research field in which considerable attention has been devoted to the study of human behaviour, offering, for instance, an updated view on cognitive biases 22 – 24 . The work on the evolution of human cooperation in particular boasts a rich mathematical modelling legacy 25 , 26 complemented by a more recent track of social dilemma experimentation 27 – 32 , as well as somewhat rarer attempts to reconcile theoretical and empirical perspectives 33 – 35 . While the basic concepts are shared with economics (cf., fitness vs. utility), evolutionary game theory introduces an extra explanatory dimension behind fitness maximisation via the process of selection. Specifically, selection describes temporal evolution towards maximum fitness during which human reasoning faculties eliminate suboptimal behaviours in a trial-and-error manner. It is largely unknown, however, if the process of selection can be manipulated by means of cognitive biases.” | senses[5] |
| control | control treatment without reward — held — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” — rules out ordinary repeated interaction as the sole source of increased cooperation — “We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatment, wherein the only actions available were cooperation ( C ) and defection ( D ), with a decoy treatment, wherein an additional action to “reward” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices:” | controls[0] |
| control | reward-parameter treatments — held — “Decoy’s relevance is perceived correctly. a Payoff matrix generalised with the reward parameter, α . Our interpretation of the results was predicated on the correct perception of the decoy as an inferior option. To test whether this was true, we increased the reward parameter from α = 3 to α = 4 to α = 5, thus decreasing the dilemma strength of the ( D , R ) pair from DS = 3 to DS = 1.5 to DS = 1, respectively. In the process, cooperation C was expected to switch places with reward R as the inferior option because dilemma strength of the ( C , D ) pair is DS = 2. b Our expectation is mirrored in the experimental data as the median frequency of C falls from 60.5% for α = 3 to 2.5% for α = 5, while the median frequency of R goes up from 3.7% for α = 3 to 76.5% for α = 5. For α = 4, similar dilemma strengths of ( D , R ) and ( C , D ) pairs (DS = 1.5 vs. DS = 2, respectively) make the distinction between C and R somewhat opaque. With the median frequency of C at 21.1% and R at 48.8%, the data seem to reflect a certain degree of confusion. Despite this confusion, R is more prevalent than C , which is in agreement with the slightly more favourable dilemma strength of the former option. The plot is a compact variant of the box-and-whisker plot in Fig. 1 and carries similar information content (medians, interquartile ranges, minimum and maximum values, and outliers if any)” — rules out misclassification of the reward option's relative value — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” | controls[1] |
| control | neutral action labels — held — “In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperation”, “defection” and “reward” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).” — rules out explicitly positive or negative framing of cooperation and defection — “In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperation”, “defection” and “reward” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).” | controls[2] |
| control | gender and academic-background checks — held — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” — rules out two measured compositional confounds — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” | controls[3] |
| audit | decoy effect —causes→ cooperation — Audit 2026-09-28: DOUBTFUL - read against its span and kept, but the reward's effect is CONSISTENT WITH the decoy effect; causes 'decoy effect' overstates an interpretation. — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” | concept_edges[0] |
| effect direction | decoy effect —causes→ cooperation — increases — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” — “in the decoy treatment is significantly higher” | concept_edges[0] |
| relation | decoy effect —causes→ cooperation — The inferior reward option shifts preference toward ordinary cooperation. — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” | concept_edges[0] |
| weight | decoy effect —causes→ cooperation — 0.95 — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” | concept_edges[0] |
| outcome | control — held — “We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatment, wherein the only actions available were cooperation ( C ) and defection ( D ), with a decoy treatment, wherein an additional action to “reward” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices:” — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | controls[0] |
| outcome | control — held — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” — “Decoy’s relevance is perceived correctly. a Payoff matrix generalised with the reward parameter, α . Our interpretation of the results was predicated on the correct perception of the decoy as an inferior option. To test whether this was true, we increased the reward parameter from α = 3 to α = 4 to α = 5, thus decreasing the dilemma strength of the ( D , R ) pair from DS = 3 to DS = 1.5 to DS = 1, respectively. In the process, cooperation C was expected to switch places with reward R as the inferior option because dilemma strength of the ( C , D ) pair is DS = 2. b Our expectation is mirrored in the experimental data as the median frequency of C falls from 60.5% for α = 3 to 2.5% for α = 5, while the median frequency of R goes up from 3.7% for α = 3 to 76.5% for α = 5. For α = 4, similar dilemma strengths of ( D , R ) and ( C , D ) pairs (DS = 1.5 vs. DS = 2, respectively) make the distinction between C and R somewhat opaque. With the median frequency of C at 21.1% and R at 48.8%, the data seem to reflect a certain degree of confusion. Despite this confusion, R is more prevalent than C , which is in agreement with the slightly more favourable dilemma strength of the former option. The plot is a compact variant of the box-and-whisker plot in Fig. 1 and carries similar information content (medians, interquartile ranges, minimum and maximum values, and outliers if any)” | controls[1] |
| outcome | control — held — “In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperation”, “defection” and “reward” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).” | controls[2] |
| outcome | control — held — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” | controls[3] |
| limitation | The decoy treatment did not make cooperation positively associated with payoff. — “In evolutionary game theory, cooperativeness prevails if it leads to success in terms of fitness or payoff. We find that in the control treatment, the average payoff per-round correlates negatively (positively) with cooperation C (defection D ). This situation improves significantly in the decoy treatment, but the improvement is insufficient to make the average payoff per-round positively (negatively) correlated with C ( D ) (Fig. 5a, b ). Our failure to clearly show that cooperativeness leads to success in the decoy treatment is puzzling and raises questions about the mechanisms underlying selection, which we address below. Interestingly, the average payoff per-round shows no correlation with R either (Fig. 5c ). This should be compared with punishment in previous experiments 29 , 30 , 32 , wherein the performance of frequent punishers was dismal. Furthermore, the cooperation-promoting effect of punishment in these experiments was unreliable 30 , 32 (but also see Ref. 38 ).” | limitations[0] |
| limitation | A framing-based interpretation remains possible outside the neutrally worded laboratory protocol. — “In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperation”, “defection” and “reward” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).” | limitations[1] |
| limitation | The proposed applied examples extrapolate beyond the tested repeated-game setting. — “Our study thus points to decoys as a means to elicit voluntary prosocial action across a spectrum of collective endeavours. A hypothetical example would be a small business team in which a member has fallen behind schedule. Although others may be reluctant to put extra hours to help their distressed colleague even if there is adequate overtime pay (the cooperative option), preferences may change by setting this overtime pay to decrease considerably some weeks before the deadline (the decoy option). Explained from such a psychological perspective, our results run the risk of appearing somewhat unsurprising. We therefore invite readers to contrast this explanation with an attempt at explaining why reward is a cooperation promoter solely within the bounds of evolutionary game theory. The latter explanation is unlikely to invoke cognitive biases as particularly relevant and would struggle with reward’s effectiveness before anyone can actually reward anyone. Deeper implications of the results for the evolution of human cooperation are admittedly less obvious (Supplementary Discussion), but with promising research directions crystallised, we believe that maintaining an optimistic perspective is warranted.” | limitations[2] |
| limitation | Later-round noise contains a residual bias toward defection. — “Returning to the question on the mechanisms underlying selection, we attempt to provide an answer by connecting several pieces of evidence. First, the results here, as well as that of a similarly structured experiment 32 , were successfully recreated in computer simulations using the data on how opponents respond to each other’s most recent actions (Supplementary Note 4 ; Supplementary Fig. 6 ). That most recent actions are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 3 . To the extent that noise cancels out, which is a first-order effect, TFT should propagate initial frequencies of cooperation C and defection D through time because C is met with C and D is met with D . We find, however, that noise fails to cancel out completely, but rather exhibits a second-order effect in the form of a bias toward defection (Supplementary Note 5 ; Supplementary Fig. 7 ). This second-order effect acts as if the decoy’s effectiveness wears off through the course of an encounter. Fortunately, at the beginning of the very next encounter, the decoy’s effectiveness is restored, causing volunteers to be more cooperative again. The overall result is that, despite the fact that volunteers correctly perceive reward R as an inferior option, the initial burst of cooperativeness caused by the decoy effect is stabilised across more than 80 rounds of the game (Fig. 2 ).” | limitations[3] |
finding · quantity · variable · definition · key-term — grounded in the full text| finding | The decoy treatment produced substantially more cooperation than the control treatment. — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.findings[0] |
| finding | The reward option changed first-round choices before participants could use it. — “Searching for mechanisms that explain improved cooperativeness in the decoy treatment, we find that reward is an effective cooperation promoter even before it can be used. Compared to the control treatment, the odds of an encounter starting with cooperation C (defection D ) are significantly improved (suppressed) (Fig. 3a ). Past the first round, response to C ( D ) in the previous round is overwhelmingly C ( D ) irrespective of the treatment (Fig. 3b, c ). Reward R is mostly met with C or an occasional R (Fig. 3d ). These results suggest that volunteers in our experiment play what can be characterised as noisy tit-for-tat (TFT) (Fig. 4 ).” | content_tags.findings[1] |
| finding | Later choices largely followed noisy tit-for-tat. — “As a cooperation promoter, reward is effective even before it can be used. a Median frequency of cooperation C in the first round of the decoy treatment (bars) is considerably higher than in the control treatment (dashed lines): 82.4% vs. 34.7%, respectively. The opposite is true of defection D : 12.0% vs. 65.3%, respectively. Volunteers in the decoy treatment also appear to be more decisive than in the control treatment as hinted by a much narrower interquartile range: e.g., for C : 21.4% vs. 47.6%, respectively. Action frequencies were calculated as in Fig. 1 . Probability densities show the frequency distributions, while cumulative densities reveal how distant these distributions are when decoy is compared to control (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.5772; p value < 10 −10 ). b – d Past the first round, response to C in the previous round is overwhelmingly C irrespective of the treatment (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.1184; p value 0.6467), response to D in the previous round is overwhelmingly D irrespective of the treatment (two-sample Kolmogorov–Smirnov test for D ; K–S statistic 0.1979; p value 0.0958), while response to R in the decoy treatment is either C or to a lesser extent R . These results suggest that the presence or absence of decoy greatly affects the first round of an encounter. In the later rounds, by contrast, volunteers play what seems to be noisy tit-for-tat” | content_tags.findings[2] |
| finding | The decoy was rarely chosen despite its large effect on cooperation. — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.findings[3] |
| finding | Participants responded to changes in the reward option's relative value in the predicted direction. — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” | content_tags.findings[4] |
| finding | Cooperation remained stable over more than eighty rounds despite a later-round bias toward defection. — “Returning to the question on the mechanisms underlying selection, we attempt to provide an answer by connecting several pieces of evidence. First, the results here, as well as that of a similarly structured experiment 32 , were successfully recreated in computer simulations using the data on how opponents respond to each other’s most recent actions (Supplementary Note 4 ; Supplementary Fig. 6 ). That most recent actions are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 3 . To the extent that noise cancels out, which is a first-order effect, TFT should propagate initial frequencies of cooperation C and defection D through time because C is met with C and D is met with D . We find, however, that noise fails to cancel out completely, but rather exhibits a second-order effect in the form of a bias toward defection (Supplementary Note 5 ; Supplementary Fig. 7 ). This second-order effect acts as if the decoy’s effectiveness wears off through the course of an encounter. Fortunately, at the beginning of the very next encounter, the decoy’s effectiveness is restored, causing volunteers to be more cooperative again. The overall result is that, despite the fact that volunteers correctly perceive reward R as an inferior option, the initial burst of cooperativeness caused by the decoy effect is stabilised across more than 80 rounds of the game (Fig. 2 ).” | content_tags.findings[5] |
| finding | The decoy treatment improved but did not reverse the payoff disadvantage associated with cooperation. — “In evolutionary game theory, cooperativeness prevails if it leads to success in terms of fitness or payoff. We find that in the control treatment, the average payoff per-round correlates negatively (positively) with cooperation C (defection D ). This situation improves significantly in the decoy treatment, but the improvement is insufficient to make the average payoff per-round positively (negatively) correlated with C ( D ) (Fig. 5a, b ). Our failure to clearly show that cooperativeness leads to success in the decoy treatment is puzzling and raises questions about the mechanisms underlying selection, which we address below. Interestingly, the average payoff per-round shows no correlation with R either (Fig. 5c ). This should be compared with punishment in previous experiments 29 , 30 , 32 , wherein the performance of frequent punishers was dismal. Furthermore, the cooperation-promoting effect of punishment in these experiments was unreliable 30 , 32 (but also see Ref. 38 ).” | content_tags.findings[6] |
| finding | Neutral wording was used to reduce framing effects from normatively loaded action labels. — “In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperation”, “defection” and “reward” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).” | content_tags.findings[7] |
| quantity | 388 — undergraduate volunteers — “We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatment, wherein the only actions available were cooperation ( C ) and defection ( D ), with a decoy treatment, wherein an additional action to “reward” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices:” | content_tags.quantities[0] |
| quantity | 60.5% — median cooperation frequency in the decoy treatment — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.quantities[1] |
| quantity | 31.4% — median cooperation frequency in the control treatment — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.quantities[2] |
| quantity | 3.70% — median frequency with which the reward decoy was selected — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.quantities[3] |
| quantity | 82.4% versus 34.7% — first-round cooperation in decoy versus control treatments — “As a cooperation promoter, reward is effective even before it can be used. a Median frequency of cooperation C in the first round of the decoy treatment (bars) is considerably higher than in the control treatment (dashed lines): 82.4% vs. 34.7%, respectively. The opposite is true of defection D : 12.0% vs. 65.3%, respectively. Volunteers in the decoy treatment also appear to be more decisive than in the control treatment as hinted by a much narrower interquartile range: e.g., for C : 21.4% vs. 47.6%, respectively. Action frequencies were calculated as in Fig. 1 . Probability densities show the frequency distributions, while cumulative densities reveal how distant these distributions are when decoy is compared to control (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.5772; p value < 10 −10 ). b – d Past the first round, response to C in the previous round is overwhelmingly C irrespective of the treatment (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.1184; p value 0.6467), response to D in the previous round is overwhelmingly D irrespective of the treatment (two-sample Kolmogorov–Smirnov test for D ; K–S statistic 0.1979; p value 0.0958), while response to R in the decoy treatment is either C or to a lesser extent R . These results suggest that the presence or absence of decoy greatly affects the first round of an encounter. In the later rounds, by contrast, volunteers play what seems to be noisy tit-for-tat” | content_tags.quantities[4] |
| variable | treatment (control versus reward-decoy condition) — “We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatment, wherein the only actions available were cooperation ( C ) and defection ( D ), with a decoy treatment, wherein an additional action to “reward” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices:” | content_tags.variables[0] |
| variable | action (cooperate, defect, or reward choice) — “In particular, action 1 (i.e., C ) meant giving up one unit for the opponent to receive two units. Action 2 (i.e., D ) meant earning one unit at the opponent’s expense of one unit. Finally, action 3 (i.e., R ) was qualitatively the same as action 1 with the distinction that one would give up two units for the opponent to receive three units in return. Further details on the experimental methods are given in the Methods section and the Supplementary Methods (see also Supplementary Figs. 1 – 3 and Supplementary Table 1). A picture emerging from this experimental setup is that reward is effective in promoting cooperation, but this effectiveness is a consequence of a cognitive bias known as the decoy effect. We therefore conclude that decoys possess an untapped potential to elicit voluntary prosocial action.” | content_tags.variables[1] |
| variable | cooperation frequency (primary behavioral outcome) — “Reward ignites cooperativeness. Median frequency of cooperation equal to 60.5% in the decoy treatment is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperation equal to 31.4% in the control treatment. Conversely, the median frequency of defection equal to 34.5% in the decoy treatment is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defection equal to 68.6% in the control treatment. These results suggest that reward as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents reward one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of action frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actions taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers” | content_tags.variables[2] |
| variable | reward parameter (manipulation of the decoy's relative value) — “Our interpretation of the effectiveness of reward R is predicated on the correct perception of how valuable R is relative to cooperation C . We tested this perception in additional treatments in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameter α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strength of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatment is therefore truly attributable to a cognitive bias, specifically, the decoy effect. To account for all eventualities, we also examined how the results between treatments change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).” | content_tags.variables[3] |
| variable | payoff per-round (individual success outcome) — “In evolutionary game theory, cooperativeness prevails if it leads to success in terms of fitness or payoff. We find that in the control treatment, the average payoff per-round correlates negatively (positively) with cooperation C (defection D ). This situation improves significantly in the decoy treatment, but the improvement is insufficient to make the average payoff per-round positively (negatively) correlated with C ( D ) (Fig. 5a, b ). Our failure to clearly show that cooperativeness leads to success in the decoy treatment is puzzling and raises questions about the mechanisms underlying selection, which we address below. Interestingly, the average payoff per-round shows no correlation with R either (Fig. 5c ). This should be compared with punishment in previous experiments 29 , 30 , 32 , wherein the performance of frequent punishers was dismal. Furthermore, the cooperation-promoting effect of punishment in these experiments was unreliable 30 , 32 (but also see Ref. 38 ).” | content_tags.variables[4] |
| definition | decoy effect — “Neoclassical economics has ascribed human actions to a relentless rational drive to maximise the (expected) utility 1 – 5 , even as the economic models struggled to account for the full range of displayed behaviours 6 – 8 . The apparent discrepancy between theory and reality ultimately gave birth to the field of behavioural economics, which has since amassed indisputable evidence to the effect that various cognitive biases stand in the way of the completely rational behaviour of economic agents 9 – 12 . Our focus is on the decoy effect, also known as the asymmetric dominance effect 13 or the attraction effect 14 , which appears in multiple-choice situations in which a particular choice called “decoy” shares some defining characteristics with another choice called “target”, but is inferior to the target in one defining characteristic 15 . Because we apply the concept of decoy in the novel context of evolutionary game theory, it is crucial to establish which defining (shared and inferior) characteristics are relevant to this context, as will be done in a moment. We emphasise for now that while decoys should be inconsequential to decision-making, they have been found to increase the attractiveness of the target, even in real-world political elections 16 . The effect’s strength, however, seems to diminish in the presence of more meaningful stimulus descriptions 17 . Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effect 18 – 21 .” | content_tags.definitions[0] |
| definition | selection — “Apart from behavioural economics, evolutionary game theory is another research field in which considerable attention has been devoted to the study of human behaviour, offering, for instance, an updated view on cognitive biases 22 – 24 . The work on the evolution of human cooperation in particular boasts a rich mathematical modelling legacy 25 , 26 complemented by a more recent track of social dilemma experimentation 27 – 32 , as well as somewhat rarer attempts to reconcile theoretical and empirical perspectives 33 – 35 . While the basic concepts are shared with economics (cf., fitness vs. utility), evolutionary game theory introduces an extra explanatory dimension behind fitness maximisation via the process of selection. Specifically, selection describes temporal evolution towards maximum fitness during which human reasoning faculties eliminate suboptimal behaviours in a trial-and-error manner. It is largely unknown, however, if the process of selection can be manipulated by means of cognitive biases.” | content_tags.definitions[1] |
| definition | dilemma strength — “How do we generally determine which action choice is worse and which is better? If our interest was solely in single-shot games, then Eq. ( 1 ) would indicate that—in a game-theoretic sense—defection D dominates over cooperation C , and both D and C dominate over reward R . This is seen from the bilateral payoff matrix in which payoffs associated with D ( C ) are higher than the corresponding payoffs associated with C ( R ). Unfortunately, game repetitions complicate matters, forcing us to consider (i) the nature of the social dilemma and (ii) the effect of repetitions. The nature of the dilemma is distilled in the concept of dilemma strength 25 , 36 . For example, by taking a difference between payoffs obtained for successful defection and mutual cooperation, and then normalising by the difference in payoffs obtained for mutual cooperation and mutual defection, we quantify how “lucrative” defection is relative to cooperation. Accordingly, the stronger the dilemma, the easier it gets for defectors to exploit cooperators (Supplementary Note 1 ; Supplementary Fig. 4 ). The effect of repetitions, by contrast, is to potentially change the nature of the dilemma 37 , at least in a probabilistic sense (Supplementary Note 2 ; Supplementary Fig. 5 ). This means that instead of having defection D as the only evolutionarily stable strategy (ESS), cooperation C may also become an ESS. For cooperators to prevail, their initial fraction x C * must be sufficiently high to provide protection against excessive exploitation by defectors. This initial fraction is given by the dilemma strength parameter, DS, such that x C * = q DS 1 - q , where q is the game termination probability. The higher the value of DS, the higher the initial fraction of cooperators must be for them to prevail.” | content_tags.definitions[2] |
| definition | tit-for-tat — “Tit-for-tat (i.e., conditional cooperation) is the prevailing strategy. a To calculate the fraction of tit-for-tat (TFT) actions, we looked at each encounter individually and added all instances in which C was followed by C , D by D , or—when available— R by R (solid lines). This sum was then divided by the total number of possible TFT actions (solid and dashed lines), which equals 2× (number of rounds −1). In the present example, the fraction of TFT actions is 4 5 = 0.8 . b The average fraction of TFT actions in the control treatment is high from the beginning and slowly increases over the course of 20+ encounters (intercept 0.711, 95% confidence interval [0.681–0.742]; slope 0.007, 95% confidence interval [0.004–0.009]; coefficient of determination R 2 = 0.292). Also shown is a breakdown of how much C and D contribute to the total fraction of TFT actions. c The average fraction of TFT actions in decoy and control treatments is similar (intercept 0.715, 95% confidence interval [0.694–0.735]; slope 0.007, 95% confidence interval [0.005–0.009]; coefficient of determination R 2 = 0.485). In the decoy treatment, however, the contribution of cooperative TFT actions is considerably higher than in the control treatment. Reward R contributes very little. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals” | content_tags.definitions[3] |
| concept | decoy effect — not defined in this paper's own words; preference shift induced by an inferior alternative — “Neoclassical economics has ascribed human actions to a relentless rational drive to maximise the (expected) utility 1 – 5 , even as the economic models struggled to account for the full range of displayed behaviours 6 – 8 . The apparent discrepancy between theory and reality ultimately gave birth to the field of behavioural economics, which has since amassed indisputable evidence to the effect that various cognitive biases stand in the way of the completely rational behaviour of economic agents 9 – 12 . Our focus is on the decoy effect, also known as the asymmetric dominance effect 13 or the attraction effect 14 , which appears in multiple-choice situations in which a particular choice called “decoy” shares some defining characteristics with another choice called “target”, but is inferior to the target in one defining characteristic 15 . Because we apply the concept of decoy in the novel context of evolutionary game theory, it is crucial to establish which defining (shared and inferior) characteristics are relevant to this context, as will be done in a moment. We emphasise for now that while decoys should be inconsequential to decision-making, they have been found to increase the attractiveness of the target, even in real-world political elections 16 . The effect’s strength, however, seems to diminish in the presence of more meaningful stimulus descriptions 17 . Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effect 18 – 21 .” | concepts[0] |
| concept | reward — not defined in this paper's own words; rarely selected cooperative decoy — “The presence of reward R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatment, the frequency of cooperation C (defection D ) in the decoy treatment is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that reward plays an instrumental role in promoting cooperation, yet opponents seldom use the opportunity to reward one another. Because C and R share the property of being cooperative actions, this kind of behaviour is consistent with the decoy effect as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .” | concepts[1] |
| concept | cooperation — not defined in this paper's own words; costly action benefiting another player — “In particular, action 1 (i.e., C ) meant giving up one unit for the opponent to receive two units. Action 2 (i.e., D ) meant earning one unit at the opponent’s expense of one unit. Finally, action 3 (i.e., R ) was qualitatively the same as action 1 with the distinction that one would give up two units for the opponent to receive three units in return. Further details on the experimental methods are given in the Methods section and the Supplementary Methods (see also Supplementary Figs. 1 – 3 and Supplementary Table 1). A picture emerging from this experimental setup is that reward is effective in promoting cooperation, but this effectiveness is a consequence of a cognitive bias known as the decoy effect. We therefore conclude that decoys possess an untapped potential to elicit voluntary prosocial action.” | concepts[2] |
| concept | defection — not defined in this paper's own words; self-benefiting action imposed at another's expense — “In particular, action 1 (i.e., C ) meant giving up one unit for the opponent to receive two units. Action 2 (i.e., D ) meant earning one unit at the opponent’s expense of one unit. Finally, action 3 (i.e., R ) was qualitatively the same as action 1 with the distinction that one would give up two units for the opponent to receive three units in return. Further details on the experimental methods are given in the Methods section and the Supplementary Methods (see also Supplementary Figs. 1 – 3 and Supplementary Table 1). A picture emerging from this experimental setup is that reward is effective in promoting cooperation, but this effectiveness is a consequence of a cognitive bias known as the decoy effect. We therefore conclude that decoys possess an untapped potential to elicit voluntary prosocial action.” | concepts[3] |
| concept | dilemma strength — not defined in this paper's own words; vulnerability of cooperation to exploitation — “How do we generally determine which action choice is worse and which is better? If our interest was solely in single-shot games, then Eq. ( 1 ) would indicate that—in a game-theoretic sense—defection D dominates over cooperation C , and both D and C dominate over reward R . This is seen from the bilateral payoff matrix in which payoffs associated with D ( C ) are higher than the corresponding payoffs associated with C ( R ). Unfortunately, game repetitions complicate matters, forcing us to consider (i) the nature of the social dilemma and (ii) the effect of repetitions. The nature of the dilemma is distilled in the concept of dilemma strength 25 , 36 . For example, by taking a difference between payoffs obtained for successful defection and mutual cooperation, and then normalising by the difference in payoffs obtained for mutual cooperation and mutual defection, we quantify how “lucrative” defection is relative to cooperation. Accordingly, the stronger the dilemma, the easier it gets for defectors to exploit cooperators (Supplementary Note 1 ; Supplementary Fig. 4 ). The effect of repetitions, by contrast, is to potentially change the nature of the dilemma 37 , at least in a probabilistic sense (Supplementary Note 2 ; Supplementary Fig. 5 ). This means that instead of having defection D as the only evolutionarily stable strategy (ESS), cooperation C may also become an ESS. For cooperators to prevail, their initial fraction x C * must be sufficiently high to provide protection against excessive exploitation by defectors. This initial fraction is given by the dilemma strength parameter, DS, such that x C * = q DS 1 - q , where q is the game termination probability. The higher the value of DS, the higher the initial fraction of cooperators must be for them to prevail.” | concepts[4] |
| concept | tit-for-tat — not defined in this paper's own words; conditional repetition of preceding actions — “Tit-for-tat (i.e., conditional cooperation) is the prevailing strategy. a To calculate the fraction of tit-for-tat (TFT) actions, we looked at each encounter individually and added all instances in which C was followed by C , D by D , or—when available— R by R (solid lines). This sum was then divided by the total number of possible TFT actions (solid and dashed lines), which equals 2× (number of rounds −1). In the present example, the fraction of TFT actions is 4 5 = 0.8 . b The average fraction of TFT actions in the control treatment is high from the beginning and slowly increases over the course of 20+ encounters (intercept 0.711, 95% confidence interval [0.681–0.742]; slope 0.007, 95% confidence interval [0.004–0.009]; coefficient of determination R 2 = 0.292). Also shown is a breakdown of how much C and D contribute to the total fraction of TFT actions. c The average fraction of TFT actions in decoy and control treatments is similar (intercept 0.715, 95% confidence interval [0.694–0.735]; slope 0.007, 95% confidence interval [0.005–0.009]; coefficient of determination R 2 = 0.485). In the decoy treatment, however, the contribution of cooperative TFT actions is considerably higher than in the control treatment. Reward R contributes very little. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals” | concepts[5] |
| concept | selection — not defined in this paper's own words; behavioral movement toward fitness maximization — “Apart from behavioural economics, evolutionary game theory is another research field in which considerable attention has been devoted to the study of human behaviour, offering, for instance, an updated view on cognitive biases 22 – 24 . The work on the evolution of human cooperation in particular boasts a rich mathematical modelling legacy 25 , 26 complemented by a more recent track of social dilemma experimentation 27 – 32 , as well as somewhat rarer attempts to reconcile theoretical and empirical perspectives 33 – 35 . While the basic concepts are shared with economics (cf., fitness vs. utility), evolutionary game theory introduces an extra explanatory dimension behind fitness maximisation via the process of selection. Specifically, selection describes temporal evolution towards maximum fitness during which human reasoning faculties eliminate suboptimal behaviours in a trial-and-error manner. It is largely unknown, however, if the process of selection can be manipulated by means of cognitive biases.” | concepts[6] |
Full text — tagged
Exploiting a cognitive bias promotes cooperationterm in social dilemma experiments Abstract The decoy effectterm is a cognitive bias documented in behavioural economics by which the presence of a third, (partly) inferior choice causes a significant shift in people’s preference for other items. Here, we performed an experiment with human volunteers who played a variant of the repeated prisoner’s dilemma game in which the standard options of “cooperate” and “defect” are supplemented with a new, decoy option, “rewardterm”. We show that although volunteers rarely chose the decoy option, its availability sparks a significant increase in overall cooperativeness and improves the likelihood of success for cooperative individuals in this game. The presence of the decoy increased willingness of volunteers to cooperate in the first step of each game, leading to subsequent propagation of such willingness by (noisy) tit-for-tatterm. Our study thus points to decoys as a means to elicit voluntary prosocial actionterm·var across a spectrum of collective endeavours.
Introduction Neoclassical economics has ascribed human actionsterm·var to a relentless rational drive to maximise the (expected) utility 1 – 5 , even as the economic models struggled to account for the full range of displayed behaviours 6 – 8 . The apparent discrepancy between theory and reality ultimately gave birth to the field of behavioural economics, which has since amassed indisputable evidence to the effect that various cognitive biases stand in the way of the completely rational behaviour of economic agents 9 – 12 . Our focus is on the decoy effectterm, also known as the asymmetric dominance effect 13 or the attraction effect 14 , which appears in multiple-choice situations in which a particular choice called “decoy” shares some defining characteristics with another choice called “target”, but is inferior to the target in one defining characteristic 15 . Because we apply the concept of decoy in the novel context of evolutionary game theory, it is crucial to establish which defining (shared and inferior) characteristics are relevant to this context, as will be done in a moment. We emphasise for now that while decoys should be inconsequential to decision-making, they have been found to increase the attractiveness of the target, even in real-world political elections 16 . The effect’s strength, however, seems to diminish in the presence of more meaningful stimulus descriptions 17 . Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effectterm 18 – 21 .
Apart from behavioural economics, evolutionary game theory is another research field in which considerable attention has been devoted to the study of human behaviour, offering, for instance, an updated view on cognitive biases 22 – 24 . The work on the evolution of human cooperationterm in particular boasts a rich mathematical modelling legacy 25 , 26 complemented by a more recent track of social dilemma experimentation 27 – 32 , as well as somewhat rarer attempts to reconcile theoretical and empirical perspectives 33 – 35 . While the basic concepts are shared with economics (cf., fitness vs. utility), evolutionary game theory introduces an extra explanatory dimension behind fitness maximisation via the process of selectionterm. Specifically, selectionterm describes temporal evolution towards maximum fitness during which human reasoning faculties eliminate suboptimal behaviours in a trial-and-error manner. It is largely unknown, however, if the process of selectionterm can be manipulated by means of cognitive biases.
We set up an experimental attempt within the bounds of evolutionary game theory designed to observe the decoy effectterm at work. Specifically, we organised a repeated Prisoner’s Dilemma (rPD) game which, based on both theory and previous experience 32 , should cause defectionterm to considerably exceed cooperationterm. We then enriched this game with a third, decoy option to “throw off” players and get them to cooperate with one another early in the game. Finally, we asked whether such an initial burst of cooperationterm can be stabilised or whether players recognise that from a purely rational perspective the decoy option is irrelevant, leading to a gradual replacement of cooperationterm with mutual defectionterm.
We recruited 388 undergraduate volunteers (mean age = 19.8, 67.8% women) to engage in the rPD game consisting of random pairwise encounters. Each encounter lasted, on average, four rounds because after any given round, a computer system could signal the end of the encounter with 25% probability. We allowed experimental sessions to run for about 75 min, leading to approximately 20 encounters per session. The purpose of these sessions was to contrast a control treatmentterm·var, wherein the only actionsterm·var available were cooperationterm ( C ) and defectionterm ( D ), with a decoy treatmentterm·var, wherein an additional actionterm·var to “rewardterm” one another ( R ) was also available. We presented the basic rules of the rPD game to volunteers in a neutrally framed manner using the following unilateral and bilateral payoff matrices: In particular, actionterm·var 1 (i.e., C ) meant giving up one unit for the opponent to receive two units. Actionterm·var 2 (i.e., D ) meant earning one unit at the opponent’s expense of one unit. Finally, actionterm·var 3 (i.e., R ) was qualitatively the same as actionterm·var 1 with the distinction that one would give up two units for the opponent to receive three units in return. Further details on the experimental methods are given in the Methods section and the Supplementary Methods (see also Supplementary Figs. 1 – 3 and Supplementary Table 1). A picture emerging from this experimental setup is that rewardterm is effective in promoting cooperationterm, but this effectiveness is a consequence of a cognitive bias known as the decoy effectterm. We therefore conclude that decoys possess an untapped potential to elicit voluntary prosocial actionterm·var.
Results Rewardterm ignites cooperativeness The presence of rewardterm R in the rPD game ignites cooperativeness (Fig. 1 ). Compared to the control treatmentterm·var, the frequency of cooperationterm C (defectionterm D ) in the decoy treatmentterm·var is significantly higher (lower). The frequency of C is furthermore stable in time (Fig. 2 ). An immediate implication is that rewardterm plays an instrumental role in promoting cooperationterm, yet opponents seldom use the opportunity to rewardterm one another. Because C and R share the property of being cooperative actionsterm·var, this kind of behaviour is consistent with the decoy effectterm as described by behavioural economists 12 , 15 , provided that R is also an inferior alternative to C .
Rewardterm ignites cooperativeness. Median frequency of cooperationterm equal to 60.5% in the decoy treatmentterm·var is significantly higher (one-tailed Mann–Whitney U test; z -score 5.6713; p value < 10 −8 ) than the median frequency of cooperationterm equal to 31.4% in the control treatmentterm·var. Conversely, the median frequency of defectionterm equal to 34.5% in the decoy treatmentterm·var is significantly lower (one-tailed Mann–Whitney U test; z -score −6.3270; p value < 10 −9 ) than the median frequency of defectionterm equal to 68.6% in the control treatmentterm·var. These results suggest that rewardterm as the decoy option plays an instrumental role in eliciting cooperative behaviour. Despite this instrumental role, opponents rewardterm one another with the median frequency of only 3.70%. Box-and-whisker plots with notches characterise the empirical distribution of actionterm·var frequencies, obtained by counting, for each volunteer, the number of cooperative, defecting, or rewarding actionsterm·var taken and then dividing these counts by the total number of rounds played. Box height determines the interquartile range, while the horizontal line inside the box represents the median. Notches indicate the 95% confidence intervals for the median. Whiskers span would encompass 99.3% of data if the data were normally distributed. Points outside of this span are drawn as outliers Initial burst of cooperationterm caused by the decoy option is stable in time. Shown are the frequencies of all three actionsterm·var as they evolve through time in the decoy treatmentterm·var. These frequencies were obtained by counting how many volunteers chose a particular actionterm·var divided by the total number of volunteers playing. Treating the frequency of cooperationterm C as a time series, we executed the augmented Dickey–Fuller test to examine the statistical stationarity of this series. Denoting the frequency of C at time t with C t , the augmented Dickey–Fuller test consisted of two steps. First, we fitted equation C t − C t −1 = β 1 + β 2 t + β 3 C t −1 + β 4 ( C t −1 − C t −2 ) + ϵ t to the displayed data, where β i , i = 1, 2, 3, 4 are the regression coefficients, and ϵ t is a normally distributed error term with a zero mean and an unknown variance. Second, we examined which regression coefficients were significantly different from zero. The results show that β 1 = 0.4258 > 0 ( t test; t -statistic 5.420; p < 10 −6 ), β 2 = 0.0005 ≈ 0 ( t test; t -statistic 1.536; p value 0.129), β 3 = −0.7586 < 0 ( t test; t -statistic −5.583; p value < 10 −6 ), and β 4 = 0.0768 ≈ 0 ( t test; t -statistic 0.674; p value 0.502). The negative value of β 3 reflects a self-correcting nature (i.e., stationarity) of the examined time series, with the cooperation frequencyterm·var fluctuating around β 1 /(1‒(1 + β 3 )) = 0.5613. Additionally, the time series shows no significant trend ( β 2 ≈ 0) nor any autoregressive structure ( β 4 ≈ 0) How do we generally determine which actionterm·var choice is worse and which is better? If our interest was solely in single-shot games, then Eq. ( 1 ) would indicate that—in a game-theoretic sense—defectionterm D dominates over cooperationterm C , and both D and C dominate over rewardterm R . This is seen from the bilateral payoff matrix in which payoffs associated with D ( C ) are higher than the corresponding payoffs associated with C ( R ). Unfortunately, game repetitions complicate matters, forcing us to consider (i) the nature of the social dilemma and (ii) the effect of repetitions. The nature of the dilemma is distilled in the concept of dilemma strengthterm 25 , 36 . For example, by taking a difference between payoffs obtained for successful defectionterm and mutual cooperationterm, and then normalising by the difference in payoffs obtained for mutual cooperationterm and mutual defectionterm, we quantify how “lucrative” defectionterm is relative to cooperationterm. Accordingly, the stronger the dilemma, the easier it gets for defectors to exploit cooperators (Supplementary Note 1 ; Supplementary Fig. 4 ). The effect of repetitions, by contrast, is to potentially change the nature of the dilemma 37 , at least in a probabilistic sense (Supplementary Note 2 ; Supplementary Fig. 5 ). This means that instead of having defectionterm D as the only evolutionarily stable strategy (ESS), cooperationterm C may also become an ESS. For cooperators to prevail, their initial fraction x C * must be sufficiently high to provide protection against excessive exploitation by defectors. This initial fraction is given by the dilemma strengthterm parameter, DS, such that x C * = q DS 1 - q , where q is the game termination probability. The higher the value of DS, the higher the initial fraction of cooperators must be for them to prevail.
To apply the concept of dilemma strengthterm for our purpose, we recognise from Eq. ( 1 ) that R is another form of cooperationterm, more costly than C , but also more beneficial for the opponent, and we look at which of the two actionsterm·var better protects cooperators from excessive exploitation by defectors. Rationality dictates ignoring the form of cooperationterm that offers less protection, meaning that rational opponents should end up playing a 2 × 2 game consisting of either the ( C , D ) pair or the ( D , R ) pair. We find from Eq. ( 1 ) that for these pairs DS = 2 and DS = 3, respectively. A higher value of DS for pair ( D , R ) points to a less favourable dilemma and forces a conclusion that R is inferior to C . We thus learn that C and R share the defining characteristic of being cooperative actionsterm·var, but R is inferior to C in another defining characteristic, i.e., resilience to exploitation by defectors. In the context of evolutionary game theory, therefore, R as defined in Eq. ( 1 ) is a valid decoy for C .
Rewardterm’s effectiveness and a cognitive bias Searching for mechanisms that explain improved cooperativeness in the decoy treatmentterm·var, we find that rewardterm is an effective cooperationterm promoter even before it can be used. Compared to the control treatmentterm·var, the odds of an encounter starting with cooperationterm C (defectionterm D ) are significantly improved (suppressed) (Fig. 3a ). Past the first round, response to C ( D ) in the previous round is overwhelmingly C ( D ) irrespective of the treatmentterm·var (Fig. 3b, c ). Rewardterm R is mostly met with C or an occasional R (Fig. 3d ). These results suggest that volunteers in our experiment play what can be characterised as noisy tit-for-tatterm (TFT) (Fig. 4 ).
As a cooperationterm promoter, rewardterm is effective even before it can be used. a Median frequency of cooperationterm C in the first round of the decoy treatmentterm·var (bars) is considerably higher than in the control treatmentterm·var (dashed lines): 82.4% vs. 34.7%, respectively. The opposite is true of defectionterm D : 12.0% vs. 65.3%, respectively. Volunteers in the decoy treatmentterm·var also appear to be more decisive than in the control treatmentterm·var as hinted by a much narrower interquartile range: e.g., for C : 21.4% vs. 47.6%, respectively. Actionterm·var frequencies were calculated as in Fig. 1 . Probability densities show the frequency distributions, while cumulative densities reveal how distant these distributions are when decoy is compared to control (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.5772; p value < 10 −10 ). b – d Past the first round, response to C in the previous round is overwhelmingly C irrespective of the treatmentterm·var (two-sample Kolmogorov–Smirnov test for C ; K–S statistic 0.1184; p value 0.6467), response to D in the previous round is overwhelmingly D irrespective of the treatmentterm·var (two-sample Kolmogorov–Smirnov test for D ; K–S statistic 0.1979; p value 0.0958), while response to R in the decoy treatmentterm·var is either C or to a lesser extent R . These results suggest that the presence or absence of decoy greatly affects the first round of an encounter. In the later rounds, by contrast, volunteers play what seems to be noisy tit-for-tatterm Tit-for-tatterm (i.e., conditional cooperationterm) is the prevailing strategy. a To calculate the fraction of tit-for-tatterm (TFT) actionsterm·var, we looked at each encounter individually and added all instances in which C was followed by C , D by D , or—when available— R by R (solid lines). This sum was then divided by the total number of possible TFT actionsterm·var (solid and dashed lines), which equals 2× (number of rounds −1). In the present example, the fraction of TFT actionsterm·var is 4 5 = 0.8 . b The average fraction of TFT actionsterm·var in the control treatmentterm·var is high from the beginning and slowly increases over the course of 20+ encounters (intercept 0.711, 95% confidence interval [0.681–0.742]; slope 0.007, 95% confidence interval [0.004–0.009]; coefficient of determination R 2 = 0.292). Also shown is a breakdown of how much C and D contribute to the total fraction of TFT actionsterm·var. c The average fraction of TFT actionsterm·var in decoy and control treatmentsterm·var is similar (intercept 0.715, 95% confidence interval [0.694–0.735]; slope 0.007, 95% confidence interval [0.005–0.009]; coefficient of determination R 2 = 0.485). In the decoy treatmentterm·var, however, the contribution of cooperative TFT actionsterm·var is considerably higher than in the control treatmentterm·var. Rewardterm R contributes very little. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals In evolutionary game theory, cooperativeness prevails if it leads to success in terms of fitness or payoff. We find that in the control treatmentterm·var, the average payoff per-roundterm·var correlates negatively (positively) with cooperationterm C (defectionterm D ). This situation improves significantly in the decoy treatmentterm·var, but the improvement is insufficient to make the average payoff per-roundterm·var positively (negatively) correlated with C ( D ) (Fig. 5a, b ). Our failure to clearly show that cooperativeness leads to success in the decoy treatmentterm·var is puzzling and raises questions about the mechanisms underlying selectionterm, which we address below. Interestingly, the average payoff per-roundterm·var shows no correlation with R either (Fig. 5c ). This should be compared with punishment in previous experiments 29 , 30 , 32 , wherein the performance of frequent punishers was dismal. Furthermore, the cooperation-promoting effect of punishment in these experiments was unreliable 30 , 32 (but also see Ref. 38 ).
Rewardterm improves the likelihood of success for cooperators. a In the control treatmentterm·var, per-round payoff correlates negatively with cooperation frequencyterm·var (intercept 0.459, 95% confidence interval [0.369–0.549]; slope −0.452, 95% confidence interval [−0.691 to −0.212]; coefficient of determination R 2 = 0.197). This negative correlation disappears in the decoy treatmentterm·var (intercept 0.541, 95% confidence interval [0.431–0.650]; slope 0.128, 95% confidence interval [−0.0511 to 0.306]; coefficient of determination R 2 = 0.0205). In fact, the angle between the two lines is significantly positive ( F -test for the treatmentterm·var × frequency interaction; F -statistic 13.2; p value 0.0004), indicating that the decoy’s presence improves the likelihood of success for cooperators. b Because frequencies of cooperationterm and defectionterm in the control treatmentterm·var sum to unity, regression lines for cooperationterm and defectionterm in this treatmentterm·var must exhibit a mirror symmetry (intercept 0.0075, 95% confidence interval [−0.164 to 0.179]; slope 0.452, 95% confidence interval [0.212–0.691]; coefficient of determination R 2 = 0.197; cf. panel ( a )). Although the same symmetry need not hold in the decoy treatmentterm·var due to rewardterm, regression lines for cooperationterm and defectionterm are also almost an ideal mirror image of one another (intercept 0.654, 95% confidence interval [0.575–0.733]; slope −0.109, 95% confidence interval [−0.276 to 0.0577]; coefficient of determination R 2 = 0.0173; cf. panel ( a )), indicting that rewardterm worsens the likelihood of success for defectors ( F -test for the treatmentterm·var × frequency interaction; F -statistic 12.9; p value 0.0004). c Per-round payoff shows no correlation with the frequency of rewardterm (intercept 0.614, 95% confidence interval [0.552–0.676]; slope −0.0355, 95% confidence interval [−0.808 to 0.737]; coefficient of determination R 2 = 0.0083), thus explaining the mirror symmetry of regression lines for cooperationterm and defectionterm in the decoy treatmentterm·var. Solid lines represent the ordinary least squares regression, whereas dashed lines are the corresponding 95% prediction confidence intervals Our interpretation of the effectiveness of rewardterm R is predicated on the correct perception of how valuable R is relative to cooperationterm C . We tested this perception in additional treatmentsterm·var in which the payoff matrix from Eq. ( 1 ) was generalised with reward parameterterm·var α (Fig. 6a ), whose value was increased from α = 3 to α = 4 to α = 5. These increased values of α bring the dilemma strengthterm of the ( D , R ) pair first to DS = 1.5 and then DS = 1, thus making R increasingly superior to C . Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengthsterm (Fig. 6b ). The former option becomes more frequent than the latter as the distinction between the two becomes clearer. Increased cooperativeness in the decoy treatmentterm·var is therefore truly attributable to a cognitive bias, specifically, the decoy effectterm. To account for all eventualities, we also examined how the results between treatmentsterm·var change due to two common confounding factors (Supplementary Note 3 ): gender (Supplementary Table 2 ) and academic background (Supplementary Table 3 ).
Decoy’s relevance is perceived correctly. a Payoff matrix generalised with the reward parameterterm·var, α . Our interpretation of the results was predicated on the correct perception of the decoy as an inferior option. To test whether this was true, we increased the reward parameterterm·var from α = 3 to α = 4 to α = 5, thus decreasing the dilemma strengthterm of the ( D , R ) pair from DS = 3 to DS = 1.5 to DS = 1, respectively. In the process, cooperationterm C was expected to switch places with rewardterm R as the inferior option because dilemma strengthterm of the ( C , D ) pair is DS = 2. b Our expectation is mirrored in the experimental data as the median frequency of C falls from 60.5% for α = 3 to 2.5% for α = 5, while the median frequency of R goes up from 3.7% for α = 3 to 76.5% for α = 5. For α = 4, similar dilemma strengthsterm of ( D , R ) and ( C , D ) pairs (DS = 1.5 vs. DS = 2, respectively) make the distinction between C and R somewhat opaque. With the median frequency of C at 21.1% and R at 48.8%, the data seem to reflect a certain degree of confusion. Despite this confusion, R is more prevalent than C , which is in agreement with the slightly more favourable dilemma strengthterm of the former option. The plot is a compact variant of the box-and-whisker plot in Fig. 1 and carries similar information content (medians, interquartile ranges, minimum and maximum values, and outliers if any) Discussion Returning to the question on the mechanisms underlying selectionterm, we attempt to provide an answer by connecting several pieces of evidence. First, the results here, as well as that of a similarly structured experiment 32 , were successfully recreated in computer simulations using the data on how opponents respond to each other’s most recent actionsterm·var (Supplementary Note 4 ; Supplementary Fig. 6 ). That most recent actionsterm·var are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 3 . To the extent that noise cancels out, which is a first-order effect, TFT should propagate initial frequencies of cooperationterm C and defectionterm D through time because C is met with C and D is met with D . We find, however, that noise fails to cancel out completely, but rather exhibits a second-order effect in the form of a bias toward defectionterm (Supplementary Note 5 ; Supplementary Fig. 7 ). This second-order effect acts as if the decoy’s effectiveness wears off through the course of an encounter. Fortunately, at the beginning of the very next encounter, the decoy’s effectiveness is restored, causing volunteers to be more cooperative again. The overall result is that, despite the fact that volunteers correctly perceive rewardterm R as an inferior option, the initial burst of cooperativeness caused by the decoy effectterm is stabilised across more than 80 rounds of the game (Fig. 2 ).
Our study thus points to decoys as a means to elicit voluntary prosocial actionterm·var across a spectrum of collective endeavours. A hypothetical example would be a small business team in which a member has fallen behind schedule. Although others may be reluctant to put extra hours to help their distressed colleague even if there is adequate overtime pay (the cooperative option), preferences may change by setting this overtime pay to decrease considerably some weeks before the deadline (the decoy option). Explained from such a psychological perspective, our results run the risk of appearing somewhat unsurprising. We therefore invite readers to contrast this explanation with an attempt at explaining why rewardterm is a cooperationterm promoter solely within the bounds of evolutionary game theory. The latter explanation is unlikely to invoke cognitive biases as particularly relevant and would struggle with rewardterm’s effectiveness before anyone can actually rewardterm anyone. Deeper implications of the results for the evolution of human cooperationterm are admittedly less obvious (Supplementary Discussion), but with promising research directions crystallised, we believe that maintaining an optimistic perspective is warranted.
Methods Experimental Protocol and Execution We executed a total of 11 experimental sessions from May 2015 to April 2016 at the Behavioural Economics Lab of Yunnan University of Finance and Economics in Kunming City, China. Two sessions were dedicated to the control treatmentterm·var, three to the decoy treatmentterm·var, and additional six to testing whether volunteers correctly value rewardterm R relative to cooperationterm C . An average of 35.3 volunteers per session participated in approximately 82.0 rounds of the game over the course of 22.9 encounters. No volunteer was allowed to participate in more than one session. The experiment was coded using the z-Tree software 39 .
We split each experimental session into three stages: preparatory, main and payout. During preparations, incoming volunteers were randomly assigned to isolated computer cubicles, where they would find instructions displayed on their computer screens, followed by a pre-game test to check the basic understanding of the rPD game. Thereafter, randomised pairing of volunteers preceded a practice pairwise encounter consisting of several rounds. In each round, paired volunteers were given 30 s to select one of the available options, and then another 30 s to examine the consequences of their selectionsterm.
The main stage of the experiment entailed a continuing sequence of randomised pairing and pairwise encounters for about 75 min. To keep track of individual success, each volunteer was endowed with an initial balance of 50 units, which changed from round to round based on decisions made and the rules in Eq. ( 1 ). Final balance, if positive, was converted into a monetary payout at a rate of ¥0.2 for 1 unit. This was supplemented with a show-up fee of ¥15, for an average payout of ¥43.3, ranging between ¥15 and ¥75.2.
In designing the experimental protocol, particular attention was paid to minimise framing effects. Terms such as “cooperationterm”, “defectionterm” and “rewardterm” invariably carry positive or negative connotations which may affect behaviour during the experiment. Seeing oneself as a cooperator may boost one’s self-image, whereas seeing oneself as a defector may affront this self-image. Therefore, options available to volunteers during the experimental sessions were labelled simply “1”, “2” and “3” and described in terms of the effect on one’s own payoff, i.e., the unilateral payoff matrix in Eq. ( 1 ).
Ethics statement The experiment was approved by the Yunnan University of Finance and Economics Ethics Committee on the use of human participants in research, and carried out in accordance with all relevant guidelines. We obtained informed consent from all volunteers.
Data availability The datasets generated and analysed during the current study are available in the Open Science Framework repository, 10.17605/OSF.IO/EHJS3 40 .
Electronic supplementary material Supplementary Information File Peer Review File Acknowledgements We are grateful to Prof. Petter Holme, Prof. Xuelong Li, Dr. Yuichi Iwasaki, Dr. Peican Zhu, Dr. Jinzhuo Liu and Dr. Chen Chu for useful discussions and Chen Shen, Yini Geng, Hao Guo, Yongjuan Ma, Danyang Jia and Yuan Li for technical help. We acknowledge support from (i) the Research Grant Programme of Inamori Foundation to M.J., (ii) the National Natural Science Foundation of China (Grant nos. 31700393 and 11671348) to L.S., (iii) the National 1000 Young Talent Plan (No. W099102), the Fundamental Research Funds for the Central Universities (no. G2017KY0001), and China Computer Federation–Tencent Open Fund (No. IAGR20170119) to Z.W. and (iv) the Japan Society for the Promotion of Science (JSPS), Grant-in-Aid for Scientific Research B to Y.I. (No. 15H04423).
Author contributions Z.W., M.J., J.-H.L. Y.I. and S.B. designed the experiment. Z.W. and L.S. performed the experiment. Z.W. and M.J. analysed the data. M.J. and J.-H.L. performed mathematical and numerical analyses. All authors discussed the results and wrote the manuscript.
Competing interests The authors declare no competing interests.
Footnotes Contributor Information Zhen WangpersName, Email: w-zhen@nwpu.edu.cn.
Marko JusuppersName, Email: mjusup@gmail.com.
Lei ShipersName, Email: lshi@ynufe.edu.cn.
References Associated Data Supplementary Materials Supplementary Information File Peer Review File Data Availability Statement The datasets generated and analysed during the current study are available in the Open Science Framework repository, 10.17605/OSF.IO/EHJS3 40 .