Stochastic Evolution with Slow Learning..

This paper studies the extent to which diffusion approximations provide a reliable guide to equilibrium selection results in finite games. It is shown that they do for a class of finite games with weak learning provided that limits are taken in a certain order. The paper also shows that making mutation rates small does not in general select a unique equilibrium but making selection strong does.

Discretion, rules and volatility - commentary

Business cycles

Coveting thy neighbors fitness as a means to resolve social dilemmas

In spatial evolutionary games the fitness of each individual is traditionally determined by the payoffs it obtains upon playing the game with its neighbors. Since defection yields the highest individual benefits, the outlook for cooperators is gloomy. While network reciprocity promotes collaborative efforts, chances of averting the impending social decline are slim if the temptation to defect is strong. It is therefore of interest to identify viable mechanisms that provide additional support for the evolution of cooperation. Inspired by the fact that the environment may be just as important as inheritance for individual development, we introduce a simple switch that allows a player to either keep its original payoff or use the average payoff of all its neighbors. Depending on which payoff is higher, the influence of either option can be tuned by means of a single parameter. We show that, in general, taking into account the environment promotes cooperation. Yet coveting the fitness of one's neighbors too strongly is not optimal. In fact, cooperation thrives best only if the influence of payoffs obtained in the traditional way is equal to that of the average payoff of the neighborhood. We present results for the prisoner's dilemma and the snowdrift game, for different levels of uncertainty governing the strategy adoption process, and for different neighborhood sizes. Our approach outlines a viable route to increased levels of cooperative behavior in structured populations, but one that requires a thoughtful implementation.Comment: 10 two-column pages, 5 figures; accepted for publication in Journal of Theoretical Biolog

Self-Commitment-Institutions and Cooperation in Overlapping Generations Games

This paper focuses on a two-period OLG economy with public imperfect observability over the intergenerational cooperative dimension. Individual endowment is at free disposal and perfectly observable. In this environment we study how a new mechanism, we call Self-Commitment-Institution (SCI), outperforms personal and community enforcement in achieving higher ex-ante e¢ ciency. Social norms with and without SCI are characterized. If social norms with SCI are implemented, agents might freely dispose of their endowment. As long as they reduce their marginal gain from deviation in terms of current utility, they also credibly self-commit on intergenerational cooperation. Under quite general conditions we .nd that, even if individual strategies are still characterized by behavioral uncertainty, the introduction of SCI relaxes the inclination toward opportunistic behavior and sustains higher e¢ ciency compared to social norms without SCI. We quantify the value of SCI and investigate the role of memory with di¤erent social norms. Finally, applications on intergenerational public good games and transfer games with productive SCI are providedCooperation; Free disposal; Imperfect public monitoring; Memory; Overlapping generation game; Self-Commitment Institution;

Social Memory and Evidence from the Past

Examples of repeated destructive behavior abound throughout the history of human societies. This paper examines the role of social memory --- a society's vicarious beliefs about the past --- in creating and perpetuating destructive conflicts. We examine whether such behavior is consistent with the theory of rational strategic behavior. We analyze an infinite-horizon model in which two countries face off each period in an extended Prisoner's Dilemma game in which an additional possibility of mutually destructive ``all out war'' yields catastrophic consequence for both sides. Each country is inhabited by a dynastic sequence of individuals who care about future individuals in the same country, and can communicate with the next generation of their countrymen using private messages. The two countries' actions in each period also produce physical evidence; a sequence of informative but imperfect public signals that can be observed by all current and future individuals. We find that, provided the future is sufficiently important for all individuals, regardless of the precision of physical evidence from the past there is an equilibrium of the model in which the two countries' social memory is systematically wrong, and in which the two countries engage in all out war with arbitrarily high frequency. Surprisingly, we find that degrading the quality of information that individuals have about current decisions may ``improve'' social memory so that it can no longer be systematically wrong. This in turn ensures that arbitrarily frequent all out wars cannot take place.Social Memory, Private Communication, Dynastic Games, Physical Evidence