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The Value Of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration

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  • Abraham Neyman

Abstract

It is known that the value of a zero-sum infinitely repeated game with incomplete information on both sides need not exist [Aumann Maschler 95]. It is proved that any number between the minmax and the maxmin of the zero-sum infinitely repeated game with incomplete information on both sides is the value of the long finitely repeated game where players' information about the uncertain number of repetitions is asymmetric.

Suggested Citation

  • Abraham Neyman, 2009. "The Value Of Two-Person Zero-Sum Repeated Games with Incomplete Information and Uncertain Duration," Discussion Paper Series dp512, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
  • Handle: RePEc:huj:dispap:dp512
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    References listed on IDEAS

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    1. Abraham Neyman, 2009. "The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information," Discussion Paper Series dp510, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    2. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, June.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
    3. Abraham Neyman, 1999. "Cooperation in Repeated Games when the Number of Stages is Not Commonly Known," Econometrica, Econometric Society, vol. 67(1), pages 45-64, January.
    4. 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.
    5. MERTENS, Jean-François & ZAMIR, Shmuel, 1977. "The maximal variation of a bounded martingale," CORE Discussion Papers RP 309, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154 Elsevier.
    7. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.
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    Cited by:

    1. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications, Elsevier.
    2. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    3. Abraham Neyman & Sylvain Sorin, 2010. "Repeated games with public uncertain duration process," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 29-52, March.

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