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Theoretical models suggest a relationship between cooperation and the prime numbers. In environments where agents play multiple one-shot prisoner's dilemma games per generation, cooperators evolve to fixation more frequently when cooperating on a cyclical schedule with a prime-number period length. This finding parrots classic predator-prey models showing selection for prime-number prey life cycles. Here, I report an empirical test of the former models using previously published data concerning humans playing one-shot public goods games across multiple time points-i.e. an analogue to multiple one-shot prisoner's dilemma games. I find very modest evidence of cyclicality at prime-numbered time intervals, though results indicate rough agreement between theoretical predictions and observed rates of full cooperation across time points. Analyses of individual decisions find increased contributions to the public good at prime-number time points and separate placebo tests indicate a 4-in-1000 chance of spuriously estimating this effect. However, when exploratory analyses exclude low-value prime-numbered time points, the magnitude of the estimated effect decreases and the hypothesis of no effect cannot be rejected, implying that low-value, prime-number time points drive estimates, contrary to theoretical model predictions. These findings cast doubt on the hypothesis of increased cooperation at prime-number time points-at least among humans playing public goods games.

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In this paper, we examine how different governance types impact prosocial behaviors in a heterogenous society. We construct a general theoretical framework to examine a game-theoretic model to assess the ease of achieving a cooperative outcome. We then build a dynamic agent-based model to examine three distinct governance types in a heterogenous population: monitoring one's neighbors, despotic leadership, and influencing one's neighbors to adapt strategies that lead to better fitness. In our research, we find that while despotic leadership may lead towards high prosociality and high returns it does not exceed the effects of a local individual who can exert positive influence in the community. This may suggest that greater individual gains can be had by cooperating and that global hierarchical leadership may not be essential as long as influential individuals exert their influence for public good and not for public ill.

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Cooperation is essential for the survival of human society. Understanding the nature of cooperation and its underlying mechanisms is crucial for studying human behavior. This paper investigates the impact of leadership on public cooperation by employing repeated sequential public goods games, as well as by examining whether leading by example (through rewards and punishments) can promote cooperation and organizational success. The leaders were assigned randomly and were given the authority to reward or punish. As a result, (1) the leaders showed a strong tendency toward reciprocity by punishing free riders and rewarding cooperators at their own expense, which enhanced the intrinsic motivation for others to follow their example; and (2) both rewards and punishments were effective in promoting cooperation, but punishment was more effective in sustaining a high level of collaboration. Additionally, leaders preferred using rewards and were more reluctant to use punishments. These findings are crucial for creating organizational structures that foster cooperation.

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Social mindfulness and Zhongyong thinking style are of high importance when evaluating relevant co-actors in the social world. The current study investigates the influence of social mindfulness and Zhongyong thinking style on cooperative financial decision making in a public goods game among a Canadian sample. We hypothesize that higher perceived social mindfulness and higher perceived Zhongyong thinking style will increase the amount of money contributed to a joint project in a public goods game. The sample was a prolific-based online recruited sample of n = 125 Canadians. We observed a significant main effect of Zhongyong thinking style on the amount of contributed money in the public goods game. Social mindfulness did not reach significance. The influence of Zhongyong thinking style was qualified by a significant Zhongyong by gender interaction, indicating that females but not males reduced their contributions if the Zhongyong thinking style of the co-actor was manipulated as being low. It is shown that Zhongyong thinking style is also relevant in a Western cultural setting. Future research is needed, however, to investigate further the reasons for the differences between females and males.

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Cooperation in the Public Goods Game (PGG) is determined by a mixture of individual differences (e.g. personality, social preferences) and group dynamics (e.g. reciprocation, social norms). However, to our knowledge, no thorough attempt has been made to separate individual and group levels of cooperation and to quantify the variance in cooperation that can be attributed to the group level. In an analysis of 10 open datasets (total N = 4,556, 1,003 groups, 7-50 rounds), we chart the trajectory of individual and group-level variance across rounds of repeated PGGs. We find that the portion of group-level variance increases initially and plateaus around the fifth round, typically at a level between 20 and 50%. In addition, we identify four factors that increase the portion of group-level variance: (i) punishment opportunities; (ii) detailed feedback including all group members' decisions; (iii) small groups (≤4 players); and (iv) groups with homogenous social preferences.

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Previous research has primarily focused on static factors influencing cooperative behavior in social dilemmas, with less attention given to dynamic factors within group social interactions, such as positive feedback received during interactions, i.e., praise. This study, through a between-subjects online experiment with a single-factor, two-level design (praise: public praise/no praise), investigates the impact of praise on cooperative behavior changes across two rounds of a three-player public goods problem. Results revealed the following: (1) A positive correlation between individuals' contributions across two rounds and a negative correlation with the number of correct answers in rule comprehension questions were evident; for men, a correlation between rule comprehension and first-round contributions was observed. (2) Multilevel model results showed that praise, role, and rule comprehension significantly positively affected contribution changes across two rounds; gender did not significantly affect contribution changes. Specifically, under public-praise conditions, contribution changes were greater. Publicly praised individuals showed positive or negative behavior changes, while those not praised in the same group showed positive changes. Men contributed significantly more in the first round than women, with no gender difference found in contribution changes. Rule comprehension positively predicted contribution changes, indicating that more correct answers led to greater positive changes in contributions. These results not only support the inferential social learning perspective, suggesting that through praise, individuals can infer external world perceptions and self-evaluations, affecting both the praised (positively or negatively) and positively influencing non-praised individuals in the same group, but also provide a theoretical basis and intervention strategies for team and organizational management in groups.

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BACKGROUND: Quorum sensing (QS) is the ability of microorganisms to assess local clonal density by measuring the extracellular concentration of signal molecules that they produce and excrete. QS is also the only known way of bacterial communication that supports the coordination of within-clone cooperative actions requiring a certain threshold density of cooperating cells. Cooperation aided by QS communication is sensitive to cheating in two different ways: laggards may benefit from not investing in cooperation but enjoying the benefit provided by their cooperating neighbors, whereas Liars explicitly promise cooperation but fail to do so, thereby convincing potential cooperating neighbors to help them, for almost free. Given this double vulnerability to cheats, it is not trivial why QS-supported cooperation is so widespread among prokaryotes. RESULTS: We investigated the evolutionary dynamics of QS in populations of cooperators for whom the QS signal is an inevitable side effect of producing the public good itself (cue-based QS). Using spatially explicit agent-based lattice simulations of QS-aided threshold cooperation (whereby cooperation is effective only above a critical cumulative level of contributions) and three different (analytical and numerical) approximations of the lattice model, we explored the dynamics of QS-aided threshold cooperation under a feasible range of parameter values. We demonstrate three major advantages of cue-driven cooperation. First, laggards cannot wipe out cooperation under a wide range of reasonable environmental conditions, in spite of an unconstrained possibility to mutate to cheating; in fact, cooperators may even exclude laggards at high cooperation thresholds. Second, lying almost never pays off, if the signal is an inevitable byproduct (i.e., the cue) of cooperation; even very cheap fake signals are selected against. And thirdly, QS is most useful if local cooperator densities are the least predictable, i.e., if their lattice-wise mean is close to the cooperation threshold with a substantial variance. CONCLUSIONS: Comparing the results of the four different modeling approaches indicates that cue-driven threshold cooperation may be a viable evolutionary strategy for microbes that cannot keep track of past behavior of their potential cooperating partners, in spatially viscous and in well-mixed environments alike. Our model can be seen as a version of the famous greenbeard effect, where greenbeards coexist with defectors in a evolutionarily stable polymorphism. Such polymorphism is maintained by the condition-dependent trade-offs of signal production which are characteristic of cue-based QS.

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Prosocial behavior is crucial for the smooth functioning of the society. Yet, individuals differ vastly in the propensity to behave prosocially. Here, we try to explain these individual differences under normal sleep conditions without any experimental modulation of sleep. Using a portable high-density EEG, we measured the sleep data in 54 healthy adults (28 females) during a normal night's sleep at the participants' homes. To capture prosocial preferences, participants played an incentivized public goods game in which they faced real monetary consequences. The whole-brain analyses showed that a higher relative slow-wave activity (SWA, an indicator of sleep depth) in a cluster of electrodes over the right temporoparietal junction (TPJ) was associated with increased prosocial preferences. Source localization and current source density analyses further support these findings. Recent sleep deprivation studies imply that sleeping enough makes us more prosocial; the present findings suggest that it is not only sleep duration, but particularly sufficient sleep depth in the TPJ that is positively related to prosociality. Because the TPJ plays a central role in social cognitive functions, we speculate that sleep depth in the TPJ, as reflected by relative SWA, might serve as a dispositional indicator of social cognition ability, which is reflected in prosocial preferences. These findings contribute to the emerging framework explaining the link between sleep and prosocial behavior by shedding light on the underlying mechanisms.

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Some scholars find that behavioral variation in the public goods game is explained by variations in participants' understanding of how to maximize payoff and that confusion leads to cooperation. Their findings lead them to question the common assumption in behavioral economics experiments that choices reflect motivations. We conduct two experiments, in which we minimize confusion by providing participants with increased training. We also introduce a question that specifically assesses participants' understanding of payoff maximization choices. Our experimental results show that the distribution of behavior types is significantly different when participants play with computers versus humans. A significant increase in contributions is also observed when participants play with humans compared to when they play with computers. Moreover, social norms may be the main motive for contributions when playing with computers. Our findings suggest that social preferences, rather than confusion, play a crucial role in determining contributions in public goods games when playing with humans. We therefore argue that the assumption in behavioral economics experiments that choices reveal motivations is indeed valid.

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Various regions often adopt punish strategies to solve traffic congestion problems. Punishing defectors is an effective strategy to solve the first-order free-rider problem in a public goods game. But this behavior is costly because the punisher is often also involved in the original joint venture and therefore vulnerable, which jeopardizes the effectiveness of this incentive. As an option, we could hire special players whose sole duty would be to monitor the population and punish defectors. The fines collected by various regions will also be used to subsidize the construction of public transportation. Thereby, we derive inspiration, and propose an improved public goods game model based on bonus and mercenary punishment. Research has shown that after cooperator gives the punisher an appropriate bonus, cooperators can strengthen the punisher, thereby weakening the defector's advantage and indirectly promoting cooperation by stabilizing the punisher's position in the system. In addition, the mechanism of reusing the fines collected from defectors and then subsidize to other players in the system can directly promote the emergence of cooperation.

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While prosocial exclusion has been proposed as a mechanism to maintain cooperation in one-shot social dilemma games, the evolution of prosocial peer exclusion in response to the threat of antisocial peer exclusion, particularly in structured populations, remains insufficiently understood. In this study, we employ an extended spatial public goods game to investigate the evolution of prosocial peer exclusion and its impact on cooperation in the presence of both prosocial and antisocial peer exclusion. Our model encompasses four primary strategies: traditional cooperation and defection, prosocial peer exclusion targeting defectors, and antisocial peer exclusion targeting cooperators. Our findings illuminate that the presence of antisocial peer exclusion significantly disrupts network reciprocity and suppresses cooperation. However, when coexisting with prosocial peer exclusion, it does not undermine the latter's efficacy in upholding cooperation, except in scenarios with low exclusion costs Unlike the cooperation-sustaining cyclic dominance pattern observed in the exclusive presence of prosocial peer exclusion, the co-presence of prosocial and antisocial peer exclusion gives rise to more intricate pathways for maintaining cooperation. These pathways include cyclic dominance involving traditional cooperation, prosocial peer exclusion, and antisocial peer exclusion, or a similar pattern involving traditional defection and the two exclusion strategies, or even cyclic dominance among all four strategies. In essence, our study enhances the theoretical framework concerning the effectiveness of the prosocial exclusion strategy, contributing to a more comprehensive understanding of its dynamics.

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For cooperation to be beneficial, cooperators should be able to differentiate individuals who are willing to cooperate from free-riders. In the absence of kin or of familiar individuals, phenotypic similarity (e.g. in terms of language) can be used as a cue of how likely two or more individuals are to behave similarly (whether they will cooperate or free-ride). Thus, phenotypic similarity could affect cooperation. However, it is unclear whether humans respond to any type of phenotypic similarity or whether only salient phenotypic traits guide cooperation. We tested whether within-group, non-salient phenotypic similarity affects cooperation in 280, 3 to 10 year old children and in 76 young adults (mean 19.8 years old) in the UK. We experimentally manipulated the degree of phenotypic similarity in three computer-based experiments. We found no evidence of a preference for, or greater cooperation with, phenotypically similar individuals in children, even though children displayed ingroup preference. Conversely, young adults cooperated more with phenotypically similar than with phenotypically diverse individuals to themselves. Our results suggest that response to non-salient phenotypic similarity varies with age and that young adults may pay more attention to non-salient cues of diversity then children.

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Play is phylogenetically widespread, and there are many proposed theories and fitness benefits of play. However, we still need a theoretical framework that unifies our understanding of the benefits that facilitated the evolution of play in so many diverse species. Starting with von Uexküll's theory of the Umwelt (i.e., the sensory-motor worlds of animals), together with the behavior systems approach, we propose that the Umwelt is an information processing system that serves basic biological functions. During development, the Umwelt undergoes a rapid expansion in the sensory and motor stimuli it processes. We argue that play is a process that converts surplus resources into information. By increasing the information content of the developing Umwelt, play confers fitness benefits. To demonstrate that play could evolve based on its information benefits, we present a model and simulation results of the evolution of a social play learning process that provides fitness-enhancing information in adult cooperative and competitive situations. Finally, we discuss this information-theoretic framework in relation to proposed hypotheses and fitness benefits of play.

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One landmark application of evolutionary game theory is the study of social dilemmas. This literature explores why people cooperate even when there are strong incentives to defect. Much of this literature, however, assumes that interactions are symmetric. Individuals are assumed to have the same strategic options and the same potential pay-offs. Yet many interesting questions arise once individuals are allowed to differ. Here, we study asymmetry in simple coordination games. In our set-up, human participants need to decide how much of their endowment to contribute to a public good. If a group's collective contribution reaches a pre-defined threshold, all group members receive a reward. To account for possible asymmetries, individuals either differ in their endowments or their productivities. According to a theoretical equilibrium analysis, such games tend to have many possible solutions. In equilibrium, group members may contribute the same amount, different amounts or nothing at all. According to our behavioural experiment, however, humans favour the equilibrium in which everyone contributes the same proportion of their endowment. We use these experimental results to highlight the non-trivial effects of inequality on cooperation, and we discuss to which extent models of evolutionary game theory can account for these effects. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

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Do economic games show evidence of altruistic or self-interested motivations in humans? A huge body of empirical work has found contrasting results. While many participants routinely make costly decisions that benefit strangers, consistent with the hypothesis that humans exhibit a biologically novel form of altruism (or "prosociality"), many participants also typically learn to pay fewer costs with experience, consistent with self-interested individuals adapting to an unfamiliar environment. Key to resolving this debate is explaining the famous "restart effect," a puzzling enigma whereby failing cooperation in public goods games can be briefly rescued by a surprise restart. Here we replicate this canonical result, often taken as evidence of uniquely human altruism, and show that it 1) disappears when cooperation is invisible, meaning individuals can no longer affect the behavior of their groupmates, consistent with strategically motivated, self-interested, cooperation; and 2) still occurs even when individuals are knowingly grouped with computer players programmed to replicate human decisions, consistent with confusion. These results show that the restart effect can be explained by a mixture of self-interest and irrational beliefs about the game's payoffs, and not altruism. Consequently, our results suggest that public goods games have often been measuring self-interested but confused behaviors and reject the idea that conventional theories of evolution cannot explain the results of economic games.

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Animals, including humans, differ in a wide range of physical and cognitive abilities ranging from measures of running speed and physical strength to learning ability and intelligence. We consider the evolution of ability when individuals interact pairwise over their contribution to a common good. In this interaction, the contribution of each is assumed to be the best given their own ability and the contribution of their partner. Since there is a tendency for individuals to partially compensate for a low contribution by their partner, low-ability individuals can do well. As a consequence, for benefit and cost structures for which individuals have a strong response to partner's contribution, there can be selection for reduced ability. Furthermore, there can be disruptive selection on ability, leading to a bimodal distribution of ability under some modes of inheritance.

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Financial (dis)incentives (e.g., bonuses, taxes) and social incentives (e.g., public praise) have typically been proposed as methods to encourage greater cooperation for the benefit of all. However, when cooperation requires exertion of effort, such interventions might not always be effective. While incentives tend to be highly motivating when choosing to exert effort, evidence suggests that they have less of an effect on behavior during effort execution. The aim of this exploratory study was to incorporate these insights into empirical investigation of the effects of social incentives on cooperative effort. To this end, we modified a public goods game task to require effort contributions to a common good. Crucial manipulation involved incorporating social incentives into this task and linking them to (a) choices that people made or (b) effortful actions they exerted. Our findings suggest, in line with recent effort-based decision-making models, that social incentives have a stronger effect on cooperative effort when they are linked to choices that people make, rather than the actual effort they exert. This study demonstrates potential benefits of eliciting a priori declarations of cooperative effort tied to social incentives to encourage greater effort for the benefit of all.

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Leaders are critical to a team or organization, their behavior affects employees' psychology and their work effort, and then affects the efficiency and innovation of the team or organization. Previous studies have focused on the role model of leaders, ignoring the guiding role of leaders with different efforts. This paper introduces leader decision-making into the game of public goods to investigate the exemplary role of leaders in behavior decision-making. It divides them into three types by setting the investment amount of leaders to explore the mechanism of leaders' influence in behavior decision-making and behavior change of team members when facing the transformation of leaders with different investment types. This research can provide a significant reference value for enterprises and social organizations on how to play the role of leaders.

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We consider interactions between players in groups of size [Formula: see text] with payoffs that not only depend on the strategies used in the group but also fluctuate at random over time. An individual can adopt either cooperation or defection as strategy and the population is updated from one time step to the next by a birth-death event according to a Moran model. Assuming recurrent symmetric mutation and payoffs to cooperators and defectors according to the composition of the group whose expected values, variances, and covariances are of the same small order, we derive a first-order approximation for the average abundance of cooperation in the selection-mutation equilibrium. In general, we show that increasing the variance of any payoff for defection or decreasing the variance of any payoff for cooperation increases the average abundance of cooperation. As for the effect of the covariance between any payoff for cooperation and any payoff for defection, we show that it depends on the number of cooperators in the group associated with these payoffs. We study in particular the public goods game, the stag hunt game, and the snowdrift game, all social dilemmas based on random benefit b and random cost c for cooperation, which lead to correlated payoffs to cooperators and defectors within groups. We show that a decrease in the scaled variance of b or c, or an increase in their scaled covariance, makes it easier for weak selection to favor the abundance of cooperation in the stag hunt game and the snowdrift game. The same conclusion holds for the public goods game except that the variance of b has no effect on the average abundance of C. Moreover, while the mutation rate has little effect on which strategy is more abundant at equilibrium, the group size may change it at least in the stag hunt game with a larger group size making it more difficult for cooperation to be more abundant than defection under weak selection.

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Around the world, people engage in practices that involve self-inflicted pain and apparently wasted resources. Researchers theorized that these practices help stabilize within-group cooperation by assorting individuals committed to collective action. While this proposition was previously studied using existing religious practices, we provide a controlled framework for an experimental investigation of various predictions derived from this theory. We recruited 372 university students in the Czech Republic who were randomly assigned into either a high-cost or low-cost condition and then chose to play a public goods game (PGG) either in a group that wastes money to signal commitment to high contributions in the game or to play in the group without such signals. We predicted that cooperators would assort in the high-cost revealed group and that, despite these costs, they would contribute more to the common pool and earn larger individual rewards over five iterations of PGG compared with the concealed group and participants in the low-cost condition. The results showed that the assortment of cooperators was more effective in the high-cost condition and translated into larger contributions of the remaining endowment to the common pool, but participants in the low-cost revealed group earned the most. We conclude that costly signals can serve as an imperfect assorting mechanism, but the size of the costs needs to be carefully balanced with potential benefits to be profitable.