Stochastic Approximations and Differential Inclusions

Michel Benaïm, Josef Hofbauer, Sylvain Sorin
2005 SIAM Journal of Control and Optimization  
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 Benaïm 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.
doi:10.1137/s0363012904439301 fatcat:5diqofvi2fakpgjaebt7c5mnsu