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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.
wiki/convergence_of_a_class_of_simple_learning_rules_to_pure-strategy_nash_equilibria.txt · Last modified: 2016/08/25 17:00 (external edit)