We consider a basic stochastic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. Following Young's papers, we call a state stochastically stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases...

Sets closed under rational behavior were introduced by Basu and Weibull (1991) as subsets of the strategy space that contain all best replies to all strategy profiles in the set. We here consider a more restrictive notion of closure under rational behavior: a subset of the strategy space is...

In (Viossat, 2006, "The replicator dynamics does not lead to correlated equilibria", forthcoming in Games and Economic Behavior), it was shown that the replicator dynamics may eliminate all pure strategies used in correlated equilibrium, so that only strategies that do not take part in any...

Saez-Marti and Weibull [4] investigate the consequences of letting some agents play a myopic best reply to the myopic best reply in Young's [8] bargaining model. This is how they introduce "cleverness" of players. We analyze such clever agents in general finite two-player games. We show that...

A large number of individuals are randomly matched into groups, where each group plays a finite symmetric game. Individuals breed true. The expected number of surviving offspring depends on own material payoff, but may also, due to cooperative breeding and/or reproductive competition, depend on...

When subjects interact in continuous time, their ability to cooperate may dramatically increase. In an experiment, we study the impact of different time horizons on cooperation in (quasi) continuous time prisoner's dilemmas. We find that cooperation levels are similar or higher when the horizon...

A technique to determine closed-loop Nash equilibria of n-player differential games is developed when their dynamic state-control system is composed of decoupled ODEs. In particular, the theory of Lie point symmetries is exploited to achieve first integrals of such systems.

We prove that, in all finite generic extensive-form games of perfect information, a continuous-time best response dynamic always converges to a Nash equilibrium component. We show the robustness of convergence by an approximate best response dynamic: whatever the initial state and an allowed...

The standard framework for analyzing games with incomplete information models players as if they form beliefs about their opponents' beliefs about their opponents' beliefs and so on, that is, as if players have an infinite depth of reasoning. This strong assumption has nontrivial implications,...

By identifying types whose low-order beliefs - up to level li - about the state of nature coincide, we obtain quotient type spaces that are typically smaller than the original ones, preserve basic topological properties, and allow standard equilibrium analysis even under bounded reasoning. Our...