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...

We consider one-to-one matching problems under two modalities of uncertainty that differ in the way types are assigned to agents. Individuals have preferences over the possible types of the agents from the opposite market side and initially know the “name” but not the ”type” of the other...

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...

The best shot game applied to networks is a discrete model of many processes of contribution to local public goods. It has generally a wide multiplicity of equilibria that we refine through stochastic stability. In this paper we show that, depending on how we define perturbations, i.e. the...

Delayed perfect monitoring in an infinitely repeated discounted game is modelled by allocating the players to a connected and undirected network. Players observe their immediate neighbors' behavior only, but communicate over time the repeated game's history truthfully throughout the network. The...

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,...