Abstract
In 1976, Bewley and Kohlberg proved that the discounted values v λ of finite zero-sum stochastic games have a limit, as λ tends to 0, using the Tarski–Seidenberg elimination theorem from real algebraic geometry. This was a fundamental step in the development of the theory of stochastic games. The current paper provides a new and direct proof for this result, relying on the explicit description of asymptotically optimal strategies. Both approaches can be used to obtain the existence of the uniform value using the construction from Mertens and Neyman (1981).
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References
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Oliu-Barton, M. (2017). The Asymptotic Value in Finite Stochastic Games. In: Díaz, J., Kirousis, L., Ortiz-Gracia, L., Serna, M. (eds) Extended Abstracts Summer 2015. Trends in Mathematics(), vol 6. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-51753-7_14
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DOI: https://doi.org/10.1007/978-3-319-51753-7_14
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