# Event

### UTRC CDS Lecture: W. Sandholm "Large Deviations & Stochastic Stability in Evolutionary Game Theory"

Friday, November 13, 2015

2:00 p.m.

1146 A V Williams Bldg

Regina King

301 405 6576

rking12@umd.edu

**UTRC Control and Dynamical Systems Invited Lecture**

Large Deviations and Stochastic Stability in Evolutionary Game Theory

William Sandholm

Professor of Economics

University of Wisconsin

**Abstract**

Population games are a basic model of strategic interactions among large numbers of small, anonymous agents. One can model the dynamics of behavior in these games by introducing revision protocols, which specify how agents myopically decide whether and when to switch strategies. Together these objects define a Markov chain on the set of population states. This stochastic process is parameterized by the size of the population and the level of noise in agents' choices.

While analyzing this process directly is not computationally feasible, one can obtain more tractable descriptions of aggregate behavior by taking the population size and noise level to their limiting values. This talk focuses on the large deviations properties of these stochastic processes, which describe the rates at which the processes move between locally stable equilibrium states. These properties can be used in turn to characterize the asymptotic behavior of the processes' stationary distributions, and hence their stochastically stable states, which are the states whose stationary distribution weights do not vanish as the parameters are taken to their limits.

The work I will describe can be summarized as follows: If one takes either one of the parameters to its limit, one can obtain an analytical characterization of large deviations properties and stochastic stability in terms of certain control problems, but these problems can only be solved explicitly in special cases. But if one looks at double limits - following the small noise limit by the large population limit, or vice versa - then these control problems become tractable, allowing one to solve examples to their very end.

**Biography**

William H. Sandholm is Professor of Economics at the University of Wisconsin-Madison, his affiliation since earning his Ph.D. in Managerial Economics and Decision Sciences from Northwestern University in 1998. His research is in game theory, with a focus on dynamic models of learning and evolution in games. His book entitled Population Games and Evolutionary Dynamics (MIT Press, 2010) is the standard reference in its field. Sandholm received an NSF CAREER Award in 2001, and his work has been supported continuously by the National Science Foundation through the present day. He is an Associate Editor at most leading journals in economic and game theory, including Theoretical Economics, the Journal of Economic Theory, Games and Economic Behavior, and the International Journal of Game Theory, and he is a member of the Council of the Game Theory Society.