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# The interplay of emotion expressions and strategy in promoting cooperation in the iterated prisoner’s dilemma

## Abstract

The iterated prisoner’s dilemma has been used to study human cooperation for decades. The recent discovery of extortion and generous strategies renewed interest on the role of strategy in shaping behavior in this dilemma. But what if players could perceive each other’s emotional expressions? Despite increasing evidence that emotion signals influence decision making, the effects of emotion in this dilemma have been mostly neglected. Here we show that emotion expressions moderate the effect of generous strategies, increasing or reducing cooperation according to the intention communicated by the signal; in contrast, expressions by extortionists had no effect on participants’ behavior, revealing a limitation of highly competitive strategies. We provide evidence that these effects are mediated mostly by inferences about other’s intentions made from strategy and emotion. These findings provide insight into the value, as well as the limits, of behavioral strategies and emotion signals for cooperation.

## Introduction

For many decades, the prisoner’s dilemma has been the main paradigm for the study of human cooperation1,2,3. Several strategies have been identified in this dilemma that influence cooperation3,4,5,6 including, more recently, extortion and generous “zero-determinant” strategies7,8,9,10,11. However, despite increasing evidence that emotion signals can influence decision making12,13,14, the effects of emotional expressions on behavior in the prisoner’s dilemma has received considerably less attention. Here we show that emotional expressions moderate the effect of generous strategies, increasing or reducing cooperation according to the intention communicated by the emotional signal. In contrast, emotion expressions by extortionists had no effect on participants’ behavior, revealing an important limitation of highly competitive strategies. Our results indicate that these effects are mostly mediated by participants’ expectations of cooperation made from the counterpart’s strategy and emotion, but also by the participants’ emotional experiences during the interaction. These findings provide insight into the importance, relative influence, as well as the limits, of behavioral strategies and emotion signals for emergence of cooperation. The results also have important practical applications for the design of increasingly pervasive autonomous machines—such as robots, self-driving cars, drones, and personal assistants—which will inevitably rely on cooperation with humans for their success15,16,17,18,19.

In the iterated prisoner’s dilemma, two players make, in each round, a simultaneous decision to either cooperate or defect. If they both cooperate, they each receive a payoff R. If they both defect, they receive a payoff P that is lower than R. However, if one cooperates and the other defects, the defector earns the highest possible reward (T) and the cooperator the lowest (S), i.e., T > R > P > S. If the number of rounds is finite, the rational prediction is that players should always defect20; however, in practice, people often cooperate3,21 and one of the main thrusts of research in the area has been finding strategies that can promote cooperation. Recently, Press and Dyson identified a class of strategies, so-called “zero-determinant,” that include strategies that unilaterally ensure a linear relation between one player’s payoff and the counterpart’s payoff7. On one extreme, there are extortion strategies7,8,10, which enforce that the counterpart cannot earn more than the extortionist by (a) cooperating less often than the counterpart, and (b) cooperating often enough that the most profitable response for the counterpart—albeit not as profitable as for the extortionist—is to cooperate. Extortion strategies, though, are only able to succeed under constrained settings7,8, tend to be evolutionary unstable8,9 and, in practice, are punished by humans10. On the other extreme, there are generous strategies, which reward cooperation while only punishing defection mildly9. Generous strategies are outperformed in head-to-head matches with extortion strategies but, tend to dominate in evolving heterogeneous populations9 and are rewarded, in practice, by humans10,11.

Whereas counterpart strategy can explain much variance in players’ behavior in the prisoner’s dilemma3, there is growing evidence that emotion expressions are very influential in shaping human decision making12,13,14. Since emotion signals tend to occur spontaneously, researchers have suggested they can be important in identifying cooperators2223,24. Expressions of emotions serve, in fact, important social functions, such as communicating one’s mental states and goals to others25,26,27,28. There is general agreement among emotion theorists that emotions are elicited by ongoing, conscious or nonconscious, appraisal of events with respect to the individual’s beliefs and goals29,30,31. Different emotions result from different appraisals, as well as their associated patterns of physiological manifestation, action tendencies, and behavioral expressions. Expressions of emotions, therefore, reflect differentiated information about the expresser’s appraisals and goals12,13,32. Accordingly, de Melo et al.12 showed that, in the iterated prisoner’s dilemma, participants successfully inferred from emotion expressions how counterparts’ were appraising the interaction and, from this information, made inferences about counterparts’ likelihood of future cooperation.

The effects of emotion expressions in extortion and generous strategies, however, have not been studied so far. When engaging with counterparts that follow a tit-for-tat strategy—i.e., only cooperate if the other cooperated in the previous round—de Melo and Terada19 showed that participants cooperated more or less according to whether the emotion expressions signaled a cooperative (e.g., joy following mutual cooperation) or competitive intention (e.g., joy following exploitation). Tit-for-tat is an interesting strategy as it strikes a balance between rewarding cooperation by the other player and punishing if the other player defects4,5. Given its inherently contingent nature, it is perhaps unsurprising that emotions expressions, being an important source of information about others’ mental states12, have a strong moderating effect. It is not clear, though, if similar patterns will occur with highly competitive strategies (e.g., extortion) or highly cooperative strategies (e.g., generous). On the one hand, when the emotion is incongruent (e.g., cooperative emotion displays with extortion behavior), people may be more motivated to process the information being communicated by emotion13,33, which would lead to a strong effect of emotion. On the other hand, people may simply interpret incongruent emotion displays as not being genuine and dismiss them34, which would lead to no effect of emotion. Here, thus, we study the moderating effects of emotion expressions in generous and extortion strategies.

### Full anonymity

Preserving full anonymity is important to minimize any reputation effects, such as participants’ concern for retaliation due to the decisions in the experiment. To accomplish full anonymity, first, counterparts were referred to by anonymous names (e.g., “Anonymous43”) and we also did not collect other information that would allow participant identification. Second, the experiment was anonymous to experimenters in that the online pool preserves participant anonymity unless the experimenters explicitly ask for identifying information from participants, which we did not.

### Data analyses

As reported in the main text, to study the effect of strategy and emotion on cooperation, experienced emotions, and expectations of cooperation, we ran strategy × emotion ANOVAs on the respective dependent variables. To understand the dynamics of cooperation across rounds, we ran a round × strategy × emotion mixed ANOVA with a Huynh–Feldt correction to account for a violation of the sphericity assumption. To understand effect size for any main effect or interaction in the ANOVA analyses, we report corresponding partial η2 values (following Cohen’s recommendations: 0.01, small; 0.09, medium; 0.25, large). Post-hoc tests were adjusted with Bonferroni corrections. Regarding the interaction for cooperation, the conventional analysis for our 2 × 2 ANOVA tests if the means for generosity and extortion strategies cross each other at different levels of the emotion factor; this results in a P value of 0.068. However, based on our theoretical motivation, a synergistic interaction35 would be more appropriate as it tests if the mean for generosity × cooperative is higher than for any of the other combination of the factors. This triangular pattern is a better theoretical fit than a crossing pattern. Accordingly, when we run this planned contrast for the interaction, we get a P value that is less than 0.001. Independent t tests were used to study the impact of emotion per strategy. To understand the effect size for these analyses, we report the Pearson’s correlation coefficient r (following Cohen’s recommendation: 0.10, small; 0.30, medium; 0.50, large).

For the multiple mediation analyses we ran binary comparisons for strategy (extortion vs. generosity) and emotion (competitive vs. cooperative); the first level was coded as 1, and the second level as 0. The mediators were expectations of cooperation and self-reported experiences of joy, sadness, regret, and anger. The dependent variable was cooperation rate. To determine mediation, we focused on the 95% bootstrapping confidence intervals; when the interval did not include zero, it can be argued that the respective mediator played a role in mediating the corresponding effect36.

### Human-subjects protection

All experimental methods were approved by the Medical Review Board of Gifu University Graduate School of Medicine (IRB ID#2018-159). As recommended by the IRB, written informed consent was provided by choosing one of two options in the online form: (1) “I am indicating that I have read the information in the instructions for participating in this research and have had a chance to ask any questions I have about the study. I consent to participate in this research.”, or (2) “I do not consent to participate in this research.” All participants gave informed consent and, at the end, were debriefed about the experimental procedures. All the experiment protocols involving human subjects was in accordance to guidelines of the Declaration of Helsinki.

## Data availability

The authors declare that data supporting the findings of this study is available with the “Supplementary materials”.

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## Acknowledgements

This research was supported by JSPS KAKENHI Grant Number JP16KK0004, and the US Army. The content does not necessarily reflect the position or the policy of any Government, and no official endorsement should be inferred.

## Author information

Authors

### Contributions

C.M. and K.T. designed the experiment, analyzed the data, and prepared this manuscript. C.M. implemented the experimental software. K.T. ran the experiment and collected the human-subjects data.

### Corresponding author

Correspondence to Celso M. de Melo.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

Supplementary Video S1.

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de Melo, C.M., Terada, K. The interplay of emotion expressions and strategy in promoting cooperation in the iterated prisoner’s dilemma. Sci Rep 10, 14959 (2020). https://doi.org/10.1038/s41598-020-71919-6

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• DOI: https://doi.org/10.1038/s41598-020-71919-6

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