The joker effect: cooperation driven by destructive agents

Understanding the emergence of cooperation is a central issue in evolutionary game theory. The hardest setup for the attainment of cooperation in a population of individuals is the Public Goods game in which cooperative agents generate a common good at their own expenses, while defectors “free-ride” this good. Eventually this causes the exhaustion of the good, a situation which is bad for everybody. Previous results have shown that introducing reputation, allowing for volunteer participation, punishing defectors, rewarding cooperators or structuring agents, can enhance cooperation. Here we present a model which shows how the introduction of rare, malicious agents - that we term jokers - performing just destructive actions on the other agents induce bursts of cooperation. The appearance of jokers promotes a rock-paper-scissors dynamics, where jokers outbeat defectors and cooperators outperform jokers, which are subsequently invaded by defectors. Thus, paradoxically, the existence of destructive agents acting indiscriminately promotes cooperation.     

Ecological public goods games: cooperation and bifurcation

The Public Goods Game is one of the most popular models for studying the origin and maintenance of cooperation. In its simplest form, this evolutionary game has two regimes: defection goes to fixation if the multiplication factor r is smaller than the interaction group size N, whereas cooperation goes to fixation if the multiplication factor r is larger than the interaction group size N. Hauert et al. [Hauert, C., Holmes, M., Doebeli, M., 2006a. Evolutionary games and population dynamics: Maintenance of cooperation in public goods games. Proc. R. Soc. Lond. B 273, 2565-2570] have introduced the Ecological Public Goods Game by viewing the payoffs from the evolutionary game as birth rates in a population dynamic model. This results in a feedback between ecological and evolutionary dynamics: if defectors are prevalent, birth rates are low and population densities decline, which leads to smaller interaction groups for the Public Goods game, and hence to dominance of cooperators, with a concomitant increase in birth rates and population densities. This feedback can lead to stable co-existence between cooperators and defectors. Here we provide a detailed analysis of the dynamics of the Ecological Public Goods Game, showing that the model exhibits various types of bifurcations, including supercritical Hopf bifurcations, which result in stable limit cycles, and hence in oscillatory co-existence of cooperators and defectors. These results show that including population dynamics in evolutionary games can have important consequences for the evolutionary dynamics of cooperation.     

Punishment as a Means of Competition: Implications for Strong Reciprocity Theory

Strong negative reciprocity, that is, sanctions imposed on norm violators at the punisher’s own expense, has powerful cooperation-enhancing effects in both real-life and experimental game situations. However, it is plausible that punishment may obtain alternative roles depending on social context and the personality characteristics of participants. We examined the occurrence of punishing behavior among 80 subjects in a strongly competitive Public Goods game setting. Despite the punishment condition, the amount of the contributions decreased steadily during the game. The amount of contributions had no significant effect on received and imposed punishments. The results indicate that certain social contexts (in this case, intensive competition) exert modifying effects on the role that punishment takes on. Subjects punished each other in order to achieve a higher rank and a financially better outcome. Punishment primarily functioned as a means of rivalry, instead of as a way of second-order cooperation, as strong reciprocity suggests. These results indicate the need for the possible modification of the social conditions of punishment mechanisms described by the strong reciprocity theory as an evolutionary explanation of human cooperation.     

Costly signaling and cooperation.

We propose an explanation of cooperation among unrelated members of a social group in which cooperation evolves because it constitutes an honest signal of the member's quality as a mate, coalition partner or competitor, and therefore results in advantageous alliances for those signaling in this manner. Our model is framed as a multi-player public goods game that involves no repeated or assortative interactions, so that non-cooperation would be a dominant strategy if there were no signaling benefits. We show that honest signaling of underlying quality by providing a public good to group members can be evolutionarily stable, and can proliferate in a population in which it is initially rare, provided that certain plausible conditions hold, including a link between group-beneficial signaling and underlying qualities of the signaler that would be of benefit to a potential mate or alliance partner. Our model applies to a range of cooperative interactions, including unconditionally sharing individually consumable resources, participating in group raiding or defense, and punishing free-riding or other violations of social norms.     

Action being character: a promising perspective on the solution concept of game theory

The inconsistency of predictions from solution concepts of conventional game theory with experimental observations is an enduring question. These solution concepts are based on the canonical rationality assumption that people are exclusively self-regarding utility maximizers. In this article, we think this assumption is problematic and, instead, assume that rational economic agents act as if they were maximizing their implicit utilities, which turns out to be a natural extension of the canonical rationality assumption. Implicit utility is defined by a player's character to reflect his personal weighting between cooperative, individualistic, and competitive social value orientations. The player who actually faces an implicit game chooses his strategy based on the common belief about the character distribution for a general player and the self-estimation of his own character, and he is not concerned about which strategies other players will choose and will never feel regret about his decision. It is shown by solving five paradigmatic games, the Dictator game, the Ultimatum game, the Prisoner's Dilemma game, the Public Goods game, and the Battle of the Sexes game, that the framework of implicit game and its corresponding solution concept, implicit equilibrium, based on this alternative assumption have potential for better explaining people's actual behaviors in social decision making situations.     

具有Allee效应的合作进化

Allee效应对物种的续存是潜在的干扰因素,在很大程度上将增加种群局部甚至全局灭绝的可能性。对许多物种,尤其是濒临物种更容易受其影响。将Allee效应引入囚徒困境博弈模型,通过理论分析与数值模拟相结合的方法分析讨论了Allee效应对合作进化的影响。研究结果表明:在恶劣的环境条件下,Allee效应极易使物种灭绝,不利于合作进化;在相对优越的环境条件下(死亡率较低),Allee效应促进合作进化,且Allee效应强度越强,更有利于合作进化,不过种群的空间斑块占有率也会随着Allee效应强度的增强而降低,使物种最终灭绝。     

Adaptive evolution of cooperation through Darwinian dynamics in Public Goods games

The linear or threshold Public Goods game (PGG) is extensively accepted as a paradigmatic model to approach the evolution of cooperation in social dilemmas. Here we explore the significant effect of nonlinearity of the structures of public goods on the evolution of cooperation within the well-mixed population by adopting Darwinian dynamics, which simultaneously consider the evolution of populations and strategies on a continuous adaptive landscape, and extend the concept of evolutionarily stable strategy (ESS) as a coalition of strategies that is both convergent-stable and resistant to invasion. Results show (i) that in the linear PGG contributing nothing is an ESS, which contradicts experimental data, (ii) that in the threshold PGG contributing the threshold value is a fragile ESS, which cannot resist the invasion of contributing nothing, and (iii) that there exists a robust ESS of contributing more than half in the sigmoid PGG if the return rate is relatively high. This work reveals the significant effect of the nonlinearity of the structures of public goods on the evolution of cooperation, and suggests that, compared with the linear or threshold PGG, the sigmoid PGG might be a more proper model for the evolution of cooperation within the well-mixed population.     

The evolution of reciprocity in sizable groups

Recently, several authors have investigated the evolution of reciprocal altruism using the repeated prisoner's dilemma game. These models suggest that natural selection is likely to favor behavioral strategies leading to reciprocal cooperation when pairs of individuals interact repeatedly in potentially cooperative situations. Using the repeated n-person prisoner's dilemma game, we consider whether reciprocal altruism is also likely to evolve when social interactions involve more individuals. We show that the conditions that allow the evolution of reciprocal cooperation become extremely restrictive as group size increases.     

Evolutionary game theory meets social science: Is there a unifying rule for human cooperation?

Evolutionary game theory has shown that human cooperation thrives in different types of social interactions with a PD structure. Models treat the cooperative strategies within the different frameworks as discrete entities and sometimes even as contenders. Whereas strong reciprocity was acclaimed as superior to classic reciprocity for its ability to defeat defectors in public goods games, recent experiments and simulations show that costly punishment fails to promote cooperation in the IR and DR games, where classic reciprocity succeeds. My aim is to show that cooperative strategies across frameworks are capable of a unified treatment, for they are governed by a common underlying rule or norm. An analysis of the reputation and action rules that govern some representative cooperative strategies both in models and in economic experiments confirms that the different frameworks share a conditional action rule and several reputation rules. The common conditional rule contains an option between costly punishment and withholding benefits that provides alternative enforcement methods against defectors. Depending on the framework, individuals can switch to the appropriate strategy and method of enforcement. The stability of human cooperation looks more promising if one mechanism controls successful strategies across frameworks.     

Replicator dynamics of reward & reputation in public goods games

Public goods games have become the mathematical metaphor for game theoretical investigations of cooperative behavior in groups of interacting individuals. Cooperation is a conundrum because cooperators make a sacrifice to benefit others at some cost to themselves. Exploiters or defectors reap the benefits and forgo costs. Despite the fact that groups of cooperators outperform groups of defectors, Darwinian selection or utilitarian principles based on rational choice should favor defectors. In order to overcome this social dilemma, much effort has been expended for investigations pertaining to punishment and sanctioning measures against defectors. Interestingly, the complementary approach to create positive incentives and to reward cooperation has received considerably less attention—despite being heavily advocated in education and social sciences for increasing productivity or preventing conflicts. Here we show that rewards can indeed stimulate cooperation in interaction groups of arbitrary size but, in contrast to punishment, fail to stabilize it. In both cases, however, reputation is essential. The combination of reward and reputation result in complex dynamics dominated by unpredictable oscillations.     

Stochastic Heterogeneous Interaction Promotes Cooperation in Spatial Prisoner's Dilemma Game

Previous studies mostly investigate player''s cooperative behavior as affected by game time-scale or individual diversity. In this paper, by involving both time-scale and diversity simultaneously, we explore the effect of stochastic heterogeneous interaction. In our model, the occurrence of game interaction between each pair of linked player obeys a random probability, which is further described by certain distributions. Simulations on a 4-neighbor square lattice show that the cooperation level is remarkably promoted when stochastic heterogeneous interaction is considered. The results are then explained by investigating the mean payoffs, the mean boundary payoffs and the transition probabilities between cooperators and defectors. We also show some typical snapshots and evolution time series of the system. Finally, the 8-neighbor square lattice and BA scale-free network results indicate that the stochastic heterogeneous interaction can be robust against different network topologies. Our work may sharpen the understanding of the joint effect of game time-scale and individual diversity on spatial games.     

Complex transition to cooperative behavior in a structured population model

Cooperation plays an important role in the evolution of species and human societies. The understanding of the emergence and persistence of cooperation in those systems is a fascinating and fundamental question. Many mechanisms were extensively studied and proposed as supporting cooperation. The current work addresses the role of migration for the maintenance of cooperation in structured populations. This problem is investigated in an evolutionary perspective through the prisoner's dilemma game paradigm. It is found that migration and structure play an essential role in the evolution of the cooperative behavior. The possible outcomes of the model are extinction of the entire population, dominance of the cooperative strategy and coexistence between cooperators and defectors. The coexistence phase is obtained in the range of large migration rates. It is also verified the existence of a critical level of structuring beyond that cooperation is always likely. In resume, we conclude that the increase in the number of demes as well as in the migration rate favor the fixation of the cooperative behavior.     

Synergy and discounting of cooperation in social dilemmas

The emergence and maintenance of cooperation by natural selection is an enduring conundrum in evolutionary biology, which has been studied using a variety of game theoretical models inspired by different biological situations. The most widely studied games are the Prisoner's Dilemma, the Snowdrift game and by-product mutualism for pairwise interactions, as well as Public Goods games in larger groups of interacting individuals. Here, we present a general framework for cooperation in social dilemmas in which all the traditional scenarios can be recovered as special cases. In social dilemmas, cooperators provide a benefit to the group at some cost, while defectors exploit the group by reaping the benefits without bearing the costs of cooperation. Using the concepts of discounting and synergy for describing how benefits accumulate when more than one cooperator is present in a group of interacting individuals, we recover the four basic scenarios of evolutionary dynamics given by (i) dominating defection, (ii) coexistence of defectors and cooperators, (iii) dominating cooperation and (iv) bi-stability, in which cooperators and defectors cannot invade each other. Generically, for groups of three or more interacting individuals further, more complex, dynamics can occur. Our framework provides the first unifying approach to model cooperation in different kinds of social dilemmas.     

Rare but severe concerted punishment that favors cooperation

As one of the mechanisms that are supposed to explain the evolution of cooperation among unrelated individuals, costly punishment, in which altruistic individuals privately bear the cost to punish defection, suffers from such drawbacks as decreasing individuals’ welfare, inducing second-order free riding, the difficulty of catching defection, and the possibility of triggering retaliation. To improve this promising mechanism, here we propose an extended Public Goods game with rare but severe concerted punishment, in which once a defector is caught punishment is triggered and the cost of punishment is equally shared among the remainder of the group. Analytical results show that, when the probability for concerted punishment is above a threshold, cooperating is, while defecting is not, an evolutionarily stable strategy in finite populations, and that this way of punishment can considerably decrease the total cost of inhibiting defection, especially in large populations.     

Cooperation beyond the dyad: on simple models and a complex society

Players in Axelrod and Hamilton''s model of cooperation were not only in a Prisoner''s Dilemma, but by definition, they were also trapped in a dyad. But animals are rarely so restricted and even the option to interact with third parties allows individuals to escape from the Prisoner''s Dilemma into a much more interesting and varied world of cooperation, from the apparently rare ‘parcelling’ to the widespread phenomenon of market effects. Our understanding of by-product mutualism, pseudo-reciprocity and the snowdrift game is also enriched by thinking ‘beyond the dyad’. The concepts of by-product mutualism and pseudo-reciprocity force us to think again about our basic definitions of cooperative behaviour (behaviour by a single individual) and cooperation (the outcome of an interaction between two or more individuals). Reciprocity is surprisingly rare outside of humans, even among large-brained ‘intelligent’ birds and mammals. Are humans unique in having extensive cooperative interactions among non-kin and an integrated cognitive system for mediating reciprocity? Perhaps, but our best chance for finding a similar phenomenon may be in delphinids, which also live in large societies with extensive cooperative interactions among non-relatives. A system of nested male alliances in bottlenose dolphins illustrates the potential and difficulties of finding a complex system of cooperation close to our own.     

Punishing free riders: direct and indirect promotion of cooperation

Human cooperation in a large group of genetically unrelated people is an evolutionary puzzle. Despite its costly nature, cooperative behavior is commonly found in all human societies—a fact that has interested researchers from a wide range of disciplines, including biology, economics, and psychology, to name a few. Many behavioral experiments have demonstrated that cooperation within a group can be sustained when free riders are punished. We argue that punishment has both a direct effect and an indirect effect on promoting cooperation. The direct effect of punishment alters the consequences of cooperation and defection in such a way as to make a rational person prefer cooperation. The indirect effect of punishment promotes cooperation among conditional cooperators by providing the condition necessary for their cooperation (i.e., the expectation that other members will also cooperate). Here we present data from two one-shot n-person prisoner's dilemma games, demonstrating that the indirect effect of punishment complements the direct effect to increase cooperation in the game. Furthermore, we show that direct and indirect effects are robust across two forms of punishment technology: either when punishment is voluntarily provided by game players themselves or when it is exogenously provided by the experimenter.     

Does Intuition Cause Cooperation?

Recently, researchers claimed that people are intuitively inclined to cooperate with reflection causing them to behave selfishly. Empirical support for this claim came from experiments using a 4-player public goods game with a marginal return of 0.5 showing that people contributed more money to a common project when they had to decide quickly (i.e., a decision based on intuition) than when they were instructed to reflect and decide slowly. This intuitive-cooperation effect is of high scientific and practical importance because it argues against a central assumption of traditional economic and evolutionary models. The first experiment of present study was set up to examine the generality of the intuitive-cooperation effect and to further validate the experimental task producing the effect. In Experiment 1, we investigated Amazon Mechanical Turk (AMT) workers'' contributions to a 4-player public goods game with a marginal return of 0.5 while we manipulated the knowledge about the other players'' contribution to the public goods game (contribution known vs. contribution unknown), the identity of the other players (humans vs. computers randomly generating contributions) and the time constraint (time pressure/intuition vs. forced delay/reflection). However, the results of Experiment 1 failed to reveal an intuitive-cooperation effect. Furthermore, four subsequent direct replications attempts with AMT workers (Experiments 2a, 2b, 2c and Experiment 3, which was conducted with naïve/inexperienced participants) also failed to demonstrate intuitive-cooperation effects. Taken together, the results of the present study could not corroborate the idea that people are intuitively cooperative, hence suggesting that the theoretical relationship between intuition and cooperation should be further scrutinized.     

Physical attractiveness and cooperation in a prisoner's dilemma game

The modulating role of age on the relationship between physical attractiveness and cooperativeness in a prisoner's dilemma game (PDG) was investigated. Previous studies have shown that physical attractiveness is negatively related to cooperative choices among young men but not young women. Following the argument that the negative relationship between physical attractiveness and cooperation is a product of short-term mating strategies among attractive men, we predicted that this relationship is unique to young men and absent among women and older men. We tested this hypothesis with 175 participants (aged 22–69 years). The results showed that physical attractiveness was negatively related to cooperative behavior among young men but not among women or older men. We further observed that the negative relationship between physical attractiveness and cooperation among young men was particularly strong when attractiveness was judged by women.     

具资源效应的非对称“鹰鸽博弈”进化稳定分析

解释合作行为的演化一直是生命科学及社会学研究的重要问题之一。经典理论研究大都关注于合作双方对等的情况。然而,在合作系统中的合作双方通常是不对等的,由此可带来博弈双方支付的非对称并影响合作双方的合作行为。该文基于经典的"鹰鸽博弈"模型,同时考虑非对称性相互关系和资源压力的影响,建立了具有强弱之分的四策略(实力强且合作、实力强且不合作、实力弱且合作和实力弱且不合作)非对称博弈模型。结合演化博弈理论及动力系统稳定性理论分析发现:在系统达到稳定状态时,四种策略的比例变化显著地依赖于博弈双方的强弱之比、资源压力及冲突的单位成本收益。对模型的进一步分析显示,当资源充足时,实力强且合作的比例与冲突的单位成本收益负相关;而实力强且不合作、实力弱且不合作的比例都与冲突的单位成本收益正相关,并且随着系统强弱对比增加,实力强且合作及实力强且不合作的比例均增加,而实力弱且不合作的比例将减小。当资源短缺时,模型得出一个有趣的结论,即随着博弈双方的强弱之比的变化,经典的"智猪博弈"与"鹰鸽博弈"可相互转化,该结论将能为不同均衡状态之间的相互转化给出一个动力学解释。     

Cooperators benefit through reputation-based partner choice in economic games

Explaining unconditional cooperation, such as donations to charities or contributions to public goods, continues to present a problem. One possibility is that cooperation can pay through developing a reputation that makes one more likely to be chosen for a profitable cooperative partnership, a process termed competitive altruism (CA) or reputation-based partner choice. Here, we show, to our knowledge, for the first time, that investing in a cooperative reputation can bring net benefits through access to more cooperative partners. Participants played a public goods game (PGG) followed by an opportunity to select a partner for a second cooperative game. We found that those who gave more in the PGG were more often selected as desired partners and received more in the paired cooperative game. Reputational competition was even stronger when it was possible for participants to receive a higher payoff from partner choice. The benefits of being selected by a more cooperative partner outweighed the costs of cooperation in the reputation building phase. CA therefore provides an alternative to indirect reciprocity as an explanation for reputation-building behaviour. Furthermore, while indirect reciprocity depends upon individuals giving preference to those of good standing, CA can explain unconditional cooperation.