| | |
Summary: Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.
SIAM J. CONTROL OPTIM. c 2009 Society for Industrial and Applied Mathematics
Vol. 48, No. 1, pp. 373396
PAYOFF-BASED DYNAMICS FOR MULTIPLAYER WEAKLY
ACYCLIC GAMES
JASON R. MARDEN, H. PEYTON YOUNG, G¨URDAL ARSLAN§, AND
JEFF S. SHAMMA¶
Abstract. We consider repeated multiplayer games in which players repeatedly and simultane-
ously choose strategies from a finite set of available strategies according to some strategy adjustment
process. We focus on the specific class of weakly acyclic games, which is particularly relevant for
multiagent cooperative control problems. A strategy adjustment process determines how players
select their strategies at any stage as a function of the information gathered over previous stages.
Of particular interest are "payoff-based" processes in which, at any stage, players know only their
own actions and (noise corrupted) payoffs from previous stages. In particular, players do not know
the actions taken by other players and do not know the structural form of payoff functions. We
introduce three different payoff-based processes for increasingly general scenarios and prove that,
after a sufficiently large number of stages, player actions constitute a Nash equilibrium at any stage
with arbitrarily high probability. We also show how to modify player utility functions through tolls
and incentives in so-called congestion games, a special class of weakly acyclic games, to guarantee
that a centralized objective can be realized as a Nash equilibrium. We illustrate the methods with a
|
