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.

We present an experiment where participants engaged in the iterated prisoner’s dilemma with counterparts that followed extortion, and generosity strategies and showed cooperative and competitive emotion expressions. The payoff matrix we used, shown in Fig. 1A, has the following parameters: T = 7, R = 5, P = 3, and S = 2. To avoid any reputation effects, the experiment was fully anonymous—i.e., the participants were anonymous to each other and to the experimenters (please see the “Methods” section for details on how this was accomplished). Participants engaged in 20 rounds of the dilemma and were instructed that their final payoff was the sum of the points earned across all rounds. The points had real financial consequences as they would be converted to tickets for a $30 lottery (see “Methods” for details). Prior to starting the task, the participants were quizzed on these instructions and had to answer all questions correctly before proceeding.

Figure 1

Experimental task and conditions. (A) The payoff matrix for the prisoner’s dilemma. Participants engaged in 20 rounds of this task. (B) Counterpart strategies are defined by the probabilities of cooperation following a specific outcome10. We consider the extortion (starting with defection) and generosity (starting with cooperation) strategies. (C) The validated facial expressions for the counterpart’s virtual representation in the task. (D) Two emotion expression patterns were considered: cooperative (e.g., joy following mutual cooperation) and competitive (e.g., joy following participant exploitation).

Building on prior work7,8,9,10, the counterpart strategies were specified based on the probability of cooperation following each possible outcome of the prisoner’s dilemma; specifically, we followed the methodology of Hilbe et al.10 to define the probabilities shown in Fig. 1B. Please see the Supplemental Information (SI) for details and proof that the proposed strategies meet the requirements for zero-determinant strategies. The extortion strategy only cooperated with a 69.2% chance following mutual cooperation and 53.8% chance after exploiting the participant; otherwise, it would defect (including in the first round). The generosity strategy cooperated in the first round and when the counterpart cooperated in the previous round; moreover, it would still cooperate with a 18.2% chance after being exploited by the participant and 36.4% chance following mutual defection. Participants were instructed they would engage in the task with other participants but, to increase experimental control and implement these strategies precisely, participants engaged with a computer script. Similar methods have been used in previous research15,19, all experimental procedures were approved by the Gifu University IRB, and participants were fully debriefed at the end.

To support emotion expression, players were represented by virtual faces. Please see the SI for further details on the ecological validity of using virtual faces for this research and a brief overview of similar work using this methodology. The counterparts’ face always corresponded to a young white Caucasian character and, as shown in Fig. 1C, the facial displays showed prototypical expressions for joy, regret, and anger12,31—for a validation of the expressions with an independent participant sample and review of prior validation studies for similar expressions, please see the SI. The character and expressions were animated in real-time (please see the SI for a video S1 of the experimental software). Counterparts expressed emotion according to a cooperative and competitive orientation12, Fig. 1D: cooperative—joy following mutual cooperation, regret after exploiting the participant, anger after being exploited, and neutral otherwise; and, competitive—regret following mutual cooperation (given that it missed the opportunity to exploit the participant), joy after exploiting the participant, anger after being exploited and, neutral otherwise. After the round outcome was revealed but before seeing the counterpart’s emotional reaction, participants were asked “How do you feel about this outcome?” and were able to self-report which emotion they felt among joy, sadness, anger, regret, or neutral. The question, thus, was meant to encourage truthful reporting of experienced emotion (but see below for a question and results on whether participants believed the counterpart’s expressed emotion was genuine). Participants were instructed that they would be able to see the expressions from counterparts and vice-versa. To get insight on the inferences participants were making about the counterpart’s intentions, before the next round started, participants were asked how likely they thought the counterpart was to cooperate in the next round. Finally, after completing the task, to get further insight on whether participants were processing the emotional information, we asked, on a 1 (“Not at all”) to 7 (“Very much”) scale: “How mentally demanding was the task?”; and, “Were your counterpart’s emotions genuine?”.

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