Abstract
We consider stochastic games with uncountable state space and prove the existence of a Nash equilibrium in Markovian strategies, reached as a limit, in an appropriate sense, of finite horizon Markovian equilibria (the latter exist even with compact metric action spaces). Our approach is based on Glicksberg’s fixed-point theorem, basic measurable selection results and a generalized Fatou Lemma.
Key Words and Phrases: stochastic games, stationary and nonstationary dynamic programming, measurable selectors, Glicksberg’s fixed-point theorem, generalized Fatou’s Lemma.
2
The research described in this paper was partially supported by ONR Grant No. N00014-86-K-0220.
3
The author would like to thank E. Balder, J.-F. Mertens and R. Rosenthal for helpful comments, and particularly A. Neyman for many useful discussions.
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© 1991 Springer Science+Business Media Dordrecht
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Amir, R. (1991). On Stochastic Games with Uncountable State and Action Spaces. In: Raghavan, T.E.S., Ferguson, T.S., Parthasarathy, T., Vrieze, O.J. (eds) Stochastic Games And Related Topics. Theory and Decision Library, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3760-7_14
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DOI: https://doi.org/10.1007/978-94-011-3760-7_14
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