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Benaim, Michel
Résultat de la recherche
Learning in games with unstable equilibria
2009, Benaim, Michel, Hofbauer, Josef, Hopkins, Ed
Stochastic approximations and differential inclusions
2005, Benaim, Michel, Hofbauer, Josef, Sorin, Sylvain
The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion. The limit set theorem of Benaim and Hirsch is extended to this situation. Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems. Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play.
Robust permanence and impermanence for stochastic replicator dynamics
2008, Benaim, Michel, Hofbauer, Josef, Sandholm, William H
Stochastic approximations and differential inclusions, part II: Applications
2006, Benaim, Michel, Hofbauer, Josef, Sorin, Sylvain
We apply the theoretical results on "stochastic approximations and differential inclusions" developed in Benaim et al. [M. Benaim, 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].