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convergence_of_a_class_of_simple_learning_rules_to_pure-strategy_nash_equilibria [2016/09/01 19:15] (current)
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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)