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The datasets generated and analysed during the current study are available in the Open Science Framework repository, 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. Neoclassical economics has ascribed human actions to a relentless rational drive to maximise the expected utility 1 — 5even 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 — 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 Motivated by this finding, multiple recent studies questioned the limits of validity of the decoy effect 18 — 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 — The work on the evolution of human cooperation in particular boasts a rich mathematical modelling legacy 2526 complemented by a more recent track of social dilemma experimentation 27 — 32as well as somewhat rarer attempts to reconcile theoretical and empirical perspectives 33 — While the basic concepts are shared with economics cf.
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. We set up an experimental attempt within the bounds of evolutionary game theory designed to observe the decoy effect at work.
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. 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, action 1 i. Finally, action 3 i. 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.
The presence of reward R in the rPD game ignites cooperativeness Fig. 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. 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 1215provided that R is also an inferior alternative to C.
Median frequency of cooperation equal to Conversely, the median frequency of defection equal to 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. 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. Whiskers span would encompass Points outside of this span are drawn as outliers.
Initial burst of cooperation caused by the decoy option is stable in time. Shown are the frequencies of all three actions as they evolve through time in the decoy treatment.
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These frequencies were obtained by counting how many volunteers chose a particular action divided by the total number of volunteers playing. Treating the frequency of cooperation C as a time series, we executed the augmented Dickey—Fuller test to examine the statistical stationarity of lfi series.
Denoting the frequency of C at time t with C tthe augmented Dickey—Fuller test consisted of two steps. Second, we examined which regression coefficients were significantly different from zero. 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. 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 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 strength for our purpose, we recognise from Eq. We find from Eq. A higher value of DS for pair DR 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 leo being cooperative actions, but R is inferior to C in another defining characteristic, i. In the context of evolutionary game theory, therefore, R as defined in Eq. 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 10863 are significantly improved suppressed Fig. Past le first round, response to C D in the previous round is overwhelmingly C D irrespective of the treatment Fig. Reward R is mostly met with C or an occasional R Fig.
These results suggest that volunteers in our experiment play what can be characterised as noisy tit-for-tat TFT Fig. As a cooperation promoter, reward is effective even before it can be used. The opposite is true of defection D: Volunteers in the decoy treatment also appear to be more decisive than in the control treatment as hinted by a much narrower interquartile range: Action frequencies were calculated as pei Fig. 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.
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.
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In the decoy treatment, however, the contribution of cooperative TFT actions is considerably higher than in the control treatment. Reward R contributes very little. 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.
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. This should be compared with punishment in previous experiments 293032wherein the performance of frequent punishers was dismal.
Furthermore, the cooperation-promoting effect of punishment in these experiments was unreliable 3032 but also see Ref. Reward improves the likelihood of success for cooperators. This negative correlation disappears in the decoy treatment intercept 0. Although the same symmetry need not hold in the decoy treatment due to reward, regression lines for cooperation and defection are also almost an ideal mirror image of one another intercept 0.
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. Volunteers respond to changes in the relation between R and C as expected from the calculated dilemma strengths Fig. 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.
Our interpretation of the results was predicated on the correct perception of the decoy as an inferior option. With the median frequency of C at Despite this confusion, R is more prevalent than Cwhich 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. Returning to the question on the mechanisms underlying selection, we attempt to provide an answer by connecting several pieces of evidence.
That most recent actions are the only ones that are truly relevant is consistent with noisy TFT described in Fig. 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. 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.
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 optionpreferences 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. Deeper implications of the results for the evolution of human cooperation are admittedly less obvious Supplementary Discussionbut with promising research directions crystallised, we believe that maintaining an optimistic perspective is warranted. Two sessions were dedicated to the control treatment, three to the decoy treatment, and additional six to testing whether volunteers correctly value reward R relative to cooperation C.
An average of No volunteer was allowed to participate in more than one session. The experiment was coded using the z-Tree software We split each experimental session into three leei 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.