An operator approach to zero-sum repeated games
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We consider two person zero-sum stochastic games. The recursive formula for the valuesvλ (resp.v n) of the discounted (resp. finitely repeated) version can be written in terms of a single basic operator Φ(α,f) where α is the weight on the present payoff andf the future payoff. We give sufficient conditions in terms of Φ(α,f) and its derivative at 0 for limv n and limvλ to exist and to be equal.
We apply these results to obtain such convergence properties for absorbing games with compact action spaces and incomplete information games.
KeywordsIncomplete Information Recursive Formula Stochastic Game Repeat Game Recursive Operator
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