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Stochastic stability and large deviations in population games

17 maggio 2016 ore 12:00 - 13:00

Aula 207, Sede di Viale Romania, 32

Speaker: Mathias Staudigl , Maastricht University

Joint with William H. Sandholm (Wisconsin-Maddison)

Abstract:Evolutionary game dynamics describe the behavior of populations of myopic, strategically interacting agents who update their strategies by applying simple decision rules. The resulting game dynamics is an irreducible Markov chain on a finite state space. Most applications in this area focus on the long-run properties of such dynamics, particularly on invariant distributions. For finitely many players, the concept of a stochastically stable state has received much attention in the literature, where it has been proposed as an equilibrium selection device in games. In this paper we propose an alternative point of view of stochastic stability, focusing on games with large player sets. In this limit we provide explicit bounds for key statistics of the evolutionary game dynamic. In particular, using recent results on sample path large deviations for population processes, we provide bounds for the expected exit time from the basin of attraction of stable equilibria and the stationary distribution of the Markov chain. If time permits we will present extensions to games with continuous action spaces.