Multiplayer Games and Adaptive Convergence to Nash Equilibria

Prof. Jeff Shamma, University of California, Los Angeles, Mechanical and Aerospace Engineering Department

Consider a scenario in which multiple decision makers repeatedly play a matrix game and adjust their strategies according to observations of each other's actions. The game is noncooperative in that each player may have its own objective/utility function, and these objectives are not shared among players. A central issue is whether player strategies will converge to a Nash equilibrium. Prior work shows how convergence to a Nash equilibrium in this setting may or may not occur.

This talk presents new strategic update mechanisms that can lead to convergent behavior in previously nonconvergent cases (such as the Shapley and Jordan counterexamples) through the use of fundamental feedback control concepts. The talk also discusses implications regarding evolutionary game theory and population dynamics.

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BIOGRAPHY

Jeff S. Shamma is a Professor of Mechanical and Aerospace Engineering at the University of California, Los Angeles. He received the Ph.D. degree in Systems Science and Engineering in 1988 from the Massachusetts Institute of Technology, Department of Mechanical Engineering. He held faculty positions at the University of Minnesota, Minneapolis, and the University of Texas, Austin, before joining UCLA in 1999. He is a recipient of a 1992 NSF Young Investigator Award and the 1996 Donald P. Eckman Award of the American Automatic Control Council, and was a Plenary Speaker at the 1998 American Control Conference. His main research interest is feedback control.