Stochastic Approximations and Differential Inclusions, Part II: Applications

We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaïm et al. [M. Benaïm, J. Hofbauer, S. Sorin. 2005. Stochastic approximations and differential inclusions. SIAM J. Control Optim. 44 328–348] to several adaptive processes used in ga...

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Bibliographic Details
Published inMathematics of operations research Vol. 31; no. 4; pp. 673 - 695
Main Authors Benaim, Michel, Hofbauer, Josef, Sorin, Sylvain
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.11.2006
Institute for Operations Research and the Management Sciences
Subjects
Analysis
approachability
Approximation
Approximations
consistency
Differential analyzers
differential inclusions
Differentials
Dynamical systems
Game theory
Mathematical analysis
Mathematical constants
Mathematical functions
Mathematical theorems
Mathematical vectors
no regret
Perturbation (Mathematics)
Regret
set-valued dynamical systems
smooth fictitious play
Stochastic approximation
Stochastic control theory
Studies
France
Austria
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Summary:We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaïm et al. [M. Benaïm, J. Hofbauer, S. Sorin. 2005. Stochastic approximations and differential inclusions. SIAM J. Control Optim. 44 328–348] to several adaptive processes used in game theory, including classical and generalized approachability, no-regret potential procedures (Hart and Mas-Colell [S. Hart, A. Mas-Colell. 2003. Regret-based continuous time dynamics. Games Econom. Behav. 45 375–394]), and smooth fictitious play [D. Fudenberg, D. K. Levine. 1995. Consistency and cautious fictitious play. J. Econom. Dynam. Control 19 1065–1089].
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.1060.0213