> Abstract: Recently, there has been a growing interest in applying a game > theoretic framework to various distributed engineering systems, including > communication networks and distributed control systems. Oftentimes, Nash > equilibria are taken as an approximation to the expected operating point > of these systems. In this talk, we examine the convergence of a class of > simple learning rules to pure-strategy Nash equilibria (PSNEs). First, we > demonstrate that if all agents adopt a learning rule from this class, when > there exists at least one PSNE, they converge to a PSNE almost surely even > in the presence of heterogeneous or time-varying feedback or observation > delays under mild conditions on the games, which we call generalized > weakly acyclic games (GWAGs). Second, we show that GWAGs are the only > games for which the learning rules are guaranteed to converge to a PSNE. > In other words, for a non-GWAG, there is an initial condition, starting > with which the learning rules do not converge to a PSNE. Finally, we > consider the case where the agents do not correctly determine their payoffs > and make errors in their decisions. We illustrate that, if the probability > of making a mistake diminishes to zero arbitrarily slow, the probability > that the strategy profile of the agents belongs to the set of PSNEs tends > to one over time. > > > Bio: Richard J. La received his B.S.E.E. from the University of Maryland, > College Park in 1994 and M.S. and Ph.D. degrees in Electrical Engineering > from the University of California, Berkeley in 1997 and 2000, > respectively. From 2000 to 2001 he was with the Mathematics of > Communication Networks group at Motorola Inc,. Since 2001 he has been on > the faculty of the Department of Electrical and Computer Engineering at > the University of Maryland, where he is currently an Associate Professor.