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Uniform Value in Recursive Games

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  • Eilon Solan
  • Nicolas Vieille

Abstract

We address the problem of existence of the uniform value in recursive games. We give two existence results. (i) The uniform value is shown to exist if the state space is countable, the action sets are finite and if, for some a > 0, there are finitely many states in which the limsup value is less than a. (ii) For games with non-negative payoff function, it is sufficient that the action set of player 2 is finite. The finiteness assumption can be further weakened.

Suggested Citation

  • Eilon Solan & Nicolas Vieille, 2000. "Uniform Value in Recursive Games," Discussion Papers 1293, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1293
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    File URL: http://www.kellogg.northwestern.edu/research/math/papers/1293.pdf
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    References listed on IDEAS

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    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 1999. "Stopping Games with Randomized Strategies," Discussion Papers 1258, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Mertens, Jean-Francois, 2002. "Stochastic games," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 47, pages 1809-1832 Elsevier.
    3. repec:dau:papers:123456789/6231 is not listed on IDEAS
    4. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
    5. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, March.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, March.
    6. Nowak, Andrzej S. & Szajowski, Krzysztof, 1998. "Nonzero-sum Stochastic Games," MPRA Paper 19995, University Library of Munich, Germany, revised 1999.
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    Cited by:

    1. Xiaoxi Li & Xavier Venel, 2016. "Recursive games: uniform value, Tauberian theorem and the Mertens conjecture “ $$Maxmin=\lim v_n=\lim v_{\uplambda }$$ M a x m i n = lim v n = lim v λ ”," International Journal of Game Theory, Springer;Game Theory Society, vol. 45(1), pages 155-189, March.

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