Stochastic Approximations and Differential Inclusions, Part II: Applications

Authors:
Michel Benaïm;Josef Hofbauer;Sylvain Sorin
Affiliations:
Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, Neuchâtel, Switzerland;Department of Mathematics, University College London, London WC1E 6BT, United Kingdom and Institut für Mathematik, Universität Wien, Nordbergstrasse 15, 1090 Wien, Austria;Equipe Combinatoire et Optimisation, UFR 929, Université P. et M. Curie---Paris 6, 175 Rue du Chevaleret, 75013 Paris, France
Venue:
Mathematics of Operations Research
Year:
2006

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Abstract

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. Control19 1065--1089].