Rewards and the evolution of cooperation in public good games

Properly coordinating cooperation is relevant for resolving public good problems, such as clean energy and environmental protection. However, little is known about how individuals can coordinate themselves for a certain level of cooperation in large populations of strangers. In a typical situation, a consensus-building process rarely succeeds, owing to a lack of face and standing. The evolution of cooperation in this type of situation is studied here using threshold public good games, in which cooperation prevails when it is initially sufficient, or otherwise it perishes. While punishment is a powerful tool for shaping human behaviours, institutional punishment is often too costly to start with only a few contributors, which is another coordination problem. Here, we show that whatever the initial conditions, reward funds based on voluntary contribution can evolve. The voluntary reward paves the way for effectively overcoming the coordination problem and efficiently transforms freeloaders into cooperators with a perceived small risk of collective failure

The evolution of cooperation through institutional incentives and optional participation

Rewards and penalties are common practical tools that can be used to promote cooperation in social institutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using compulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165-1169) considered optional participation as well as institutional incentives and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full classification of these evolutionary dynamics. Specifically, whenever penalties are large enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is compulsory, these penalties will ultimately result in cooperation if participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case. We also argue that optional participation is not so effective at improving cooperation under rewards.Comment: 20 pages, 4 figure

The evolution of cooperation through institutional incentives and optimal participation

Rewards and penalties are common practical tools that can be used to promote cooperation in social intitutions. The evolution of cooperation under reward and punishment incentives in joint enterprises has been formalized and investigated, mostly by using ompulsory public good games. Recently, Sasaki et al. (2012, Proc Natl Acad Sci USA 109:1165.1169) considered optional participation as well as institutional incentive and described how the interplay between these mechanisms affects the evolution of cooperation in public good games. Here, we present a full clssification of these evolutionary dynamics. Specifically, whenever penalties are large enough to cause the bi-stability of both cooperation and defection in cases in which participation in the public good game is optional. The global stability of coercion-based cooperation in this optional case contrasts strikingly with the bi-stability that is observed in the compulsory case. We also argue that optional participation is not so effective at imrpoving cooperation under rewards

Antisocial pool rewarding does not deter public cooperation

Rewarding cooperation is in many ways expected behaviour from social players. However, strategies that promote antisocial behaviour are also surprisingly common, not just in human societies, but also among eusocial insects and bacteria. Examples include sanctioning of individuals who behave prosocially, or rewarding of freeriders who do not contribute to collective enterprises. We therefore study the public goods game with antisocial and prosocial pool rewarding in order to determine the potential negative consequences on the effectiveness of positive incentives to promote cooperation. Contrary to a naive expectation, we show that the ability of defectors to distribute rewards to their like does not deter public cooperation as long as cooperators are able to do the same. Even in the presence of antisocial rewarding the spatial selection for cooperation in evolutionary social dilemmas is enhanced. Since the administration of rewards to either strategy requires a considerable degree of aggregation, cooperators can enjoy the benefits of their prosocial contributions as well as the corresponding rewards. Defectors when aggregated, on the other hand, can enjoy antisocial rewards, but due to their lack of contributions to the public good they ultimately succumb to their inherent inability to secure a sustainable future. Strategies that facilitate the aggregation of akin players, even if they seek to promote antisocial behaviour, thus always enhance the long-term benefits of cooperation.Comment: 9 two-column pages, 5 figures; accepted for publication in Proceedings of the Royal Society

Give and you shall receive. Give more and you shall be honored. Experimental evidence for altruism as costly signaling.

In two studies, we measured the degree and manner of reciprocation of a public good in subsequent two-by-two interactions. Both studies consisted of two phases: a public good phase and a subsequent give some game (i.e. a gradual Prisoner's dilemma game). In the first study, the public good was a financial game in the lab. In the second study, the public good games were real life student projects. The observed behavior in the subsequent interactions was consistent with the reciprocity rule, but only up to the fairness norm of equality. Students who had invested more than their fair share, did not receive more financial returns than those who had invested a fair share. However, despite the lack of financial benefits, these high investors were preferred more as future team mates (Study 1), or received more social rewards (Study 2). We interpret these findings in terms of altruism as costly signaling.Altruism; Cooperation; Costly signaling; Prisoner's dilemma game; Reputations; Studies;

Optimal distribution of incentives for public cooperation in heterogeneous interaction environments

In the framework of evolutionary games with institutional reciprocity, limited incentives are at disposal for rewarding cooperators and punishing defectors. In the simplest case, it can be assumed that, depending on their strategies, all players receive equal incentives from the common pool. The question arises, however, what is the optimal distribution of institutional incentives? How should we best reward and punish individuals for cooperation to thrive? We study this problem for the public goods game on a scale-free network. We show that if the synergetic effects of group interactions are weak, the level of cooperation in the population can be maximized simply by adopting the simplest "equal distribution" scheme. If synergetic effects are strong, however, it is best to reward high-degree nodes more than low-degree nodes. These distribution schemes for institutional rewards are independent of payoff normalization. For institutional punishment, however, the same optimization problem is more complex, and its solution depends on whether absolute or degree-normalized payoffs are used. We find that degree-normalized payoffs require high-degree nodes be punished more lenient than low-degree nodes. Conversely, if absolute payoffs count, then high-degree nodes should be punished stronger than low-degree nodes.Comment: 19 pages, 8 figures; accepted for publication in Frontiers in Behavioral Neuroscienc

Correlation of Positive and Negative Reciprocity Fails to Confer an Evolutionary Advantage: Phase Transitions to Elementary Strategies

Economic experiments reveal that humans value cooperation and fairness. Punishing unfair behavior is therefore common, and according to the theory of strong reciprocity, it is also directly related to rewarding cooperative behavior. However, empirical data fail to confirm that positive and negative reciprocity are correlated. Inspired by this disagreement, we determine whether the combined application of reward and punishment is evolutionarily advantageous. We study a spatial public goods game, where in addition to the three elementary strategies of defection, rewarding, and punishment, a fourth strategy that combines the latter two competes for space. We find rich dynamical behavior that gives rise to intricate phase diagrams where continuous and discontinuous phase transitions occur in succession. Indirect territorial competition, spontaneous emergence of cyclic dominance, as well as divergent fluctuations of oscillations that terminate in an absorbing phase are observed. Yet, despite the high complexity of solutions, the combined strategy can survive only in very narrow and unrealistic parameter regions. Elementary strategies, either in pure or mixed phases, are much more common and likely to prevail. Our results highlight the importance of patterns and structure in human cooperation, which should be considered in future experiments

Emergence and resilience of cooperation in the spatial Prisoner's Dilemma via a reward mechanism

We study the problem of the emergence of cooperation in the spatial Prisoner's Dilemma. The pioneering work by Nowak and May showed that large initial populations of cooperators can survive and sustain cooperation in a square lattice with imitate-the-best evolutionary dynamics. We revisit this problem in a cost-benefit formulation suitable for a number of biological applications. We show that if a fixed-amount reward is established for cooperators to share, a single cooperator can invade a population of defectors and form structures that are resilient to re-invasion even if the reward mechanism is turned off. We discuss analytically the case of the invasion by a single cooperator and present agent-based simulations for small initial fractions of cooperators. Large cooperation levels, in the sustainability range, are found. In the conclusions we discuss possible applications of this model as well as its connections with other mechanisms proposed to promote the emergence of cooperation