Asymptotically Optimal Strategies for Adaptive Zero-Sum Discounted Markov Games

We consider a class of discrete-time two person zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs. The game evolves according to the recursive equation ..., where the disturbance process ... is formed by independent and identically distributed R^sup k^-valued r...

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Bibliographic Details
Published in:SIAM journal on control and optimization 2009-01, Vol.48 (3), p.1405-1421
Main Authors: Minjárez-Sosa, J. Adolfo, Vega-Amaya, Oscar
Format: Article
Language:English
Subjects:
Asymptotic methods
Asymptotic properties
Density
Game theory
Games
Markov analysis
Markov processes
Mathematical analysis
Optimization
Players
Strategy
Studies
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Summary:We consider a class of discrete-time two person zero-sum Markov games with Borel state and action spaces, and possibly unbounded payoffs. The game evolves according to the recursive equation ..., where the disturbance process ... is formed by independent and identically distributed R^sup k^-valued random vectors, which are observable but whose common density ρ is unknown to both players. Under certain continuity and compactness conditions, we combine a nonstationary iteration procedure and suitable density estimation methods to construct asymptotically discounted optimal strategies for both players. [PUBLICATION ABSTRACT]
ISSN:0363-0129
1095-7138
DOI:10.1137/060651458