Stochastic approximations and differential inclusions
Author(s)
Date issued
2005
In
Siam Journal on Control and Optimization
Vol
1
No
44
From page
328
To page
348
Subjects
stochastic approximation differential inclusions set-valued dynamical systems chain recurrence approachability game theory learning fictitious play FICTITIOUS PLAY DYNAMICAL-SYSTEMS GAMES CONVERGENCE ALGORITHMS
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 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.
Publication type
journal article
File(s)