Coalitional stochastic stability in games, networks and markets

- This paper unifies stochastic stability analysis in non-cooperative and cooperative settings.
- We examine a dynamic process of unilateral and joint deviations of agents.
- We characterize stochastically stable states under the logit choice rule.
- We provide results in cooperative settings analogous to those in non-cooperative ones.
- We apply our results to simple exchange economies, network cost sharing problems and unanimity games.

This paper examines a dynamic process of unilateral and joint deviations of agents and the resulting stochastic evolution of social conventions. Our model unifies stochastic stability analysis in static settings, including normal form games, network formation games, and simple exchange economies, as stochastic stability analysis in a class of interactions in which agents unilaterally and jointly choose their strategies. We embed a static setting in a dynamic process; Over time agents revise their strategies based on the improvements that the new strategy profile offers them. In addition to the optimization process, there are persistent random shocks on agents' utility that potentially lead to switching to suboptimal strategies. Under a logit specification of choice probabilities, we characterize the set of states that will be observed in the long-run as noise vanishes. We apply these results to examples of certain potential games.