Applied Mathematics and Computation Seminar
Stochastic Evolutionary Game Theory: Overview and Recent Results
William Sandholm, University of Wisconsin-Madison

Abstract: Population games provide a general model of strategic interactions among large numbers of agents; network congestion, multilateral externalities, and natural selection are among their many applications. Behavior in these games is most naturally modeled as a stochastic dynamic adjustment processes. One begins with a particular game and a model of how individual agents make decisions. When the number of agents is large enough and the time horizon of interest not too long, the evolution of aggregate behavior is well approximated by solutions to the mean dynamic, an ordinary differential equation describing the expected increments of the underlying stochastic process. If one is interested in behavior over very long time spans, one studies the stochastic evolutionary processes directly, using its stationary distribution as the basis for predictions; using the large deviations methods of Freidlin and Wentzell, one can obtain unique predictions of infinite horizon behavior even when the mean dynamic admits multiple stable equilibria. In this talk, I will explain the main models of stochastic evolutionary game theory, present some recent results, and indicate directions for future research. See http://www.ssc.wisc.edu/~whs/research/egt.pdf for a survey.

Refreshments at 3:45

4:00pm–5:00pm, Tuesday, September 29, 2009 in LGRT 1634

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