Stochastic Approximations and Differential Inclusions, Part II: Applications
Mathematics of Operations Research
Time Average Replicator and Best-Reply Dynamics
Mathematics of Operations Research
Mean field limit of non-smooth systems and differential inclusions
ACM SIGMETRICS Performance Evaluation Review
A Class of Self-Interacting Processes with Applications to Games and Reinforced Random Walks
SIAM Journal on Control and Optimization
On the Convergence Rate for Stochastic Approximation in the Nonsmooth Setting
Mathematics of Operations Research
The Knowledge Engineering Review
Distributed stochastic approximation for constrained and unconstrained optimization
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
Markov chains with discontinuous drifts have differential inclusion limits
Performance Evaluation
Consistency of Vanishingly Smooth Fictitious Play
Mathematics of Operations Research
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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.