Stochastic Approximations and Differential Inclusions

Michel Benaïm (), Josef Hofbauer and Sylvain Sorin
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Michel Benaïm: UNINE - Université de Neuchâtel = University of Neuchatel

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Abstract: 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 Bena\"{\i}m 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.

Keywords: Stochastic approximation; Multivalued dynamical systems; Approximation stochastique; Système dynamique multivalue (search for similar items in EconPapers)
Date: 2003
Note: View the original document on HAL open archive server: https://hal.science/hal-00242990
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Citations: View citations in EconPapers (14)

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