convergence_of_a_class_of_simple_learning_rules_to_pure-strategy_nash_equilibria

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+ | **Convergence of a class of simple learning rules to pure-strategy Nash equilibria** | ||

+ | This is joint work with Siddharth Pal. | ||

+ | |||

+ | //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. |

convergence_of_a_class_of_simple_learning_rules_to_pure-strategy_nash_equilibria.txt ยท Last modified: 2016/09/01 19:15 (external edit)