Journal
GAMES AND ECONOMIC BEHAVIOR
Volume 70, Issue 1, Pages 71-83Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.geb.2008.11.012
Keywords
Games; Learning; Adaptive dynamics; Stochastic algorithms; Congestion games
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A stochastic process that describes a payoff-based learning procedure and the associated adaptive behavior of players in a repeated game is considered. The process is shown to converge almost surely towards a stationary state which is characterized as an equilibrium for a related game. The analysis is based on techniques borrowed from the theory of stochastic algorithms and proceeds by studying an associated continuous dynamical system which represents the evolution of the players' evaluations. An application to the case of finitely many users in a congested traffic network with parallel links is considered. Alternative descriptions for the dynamics and the corresponding rest points are discussed, including a Lagrangian representation. (C) 2008 Elsevier Inc. All rights reserved.
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