IDEAS home Printed from https://ideas.repec.org/p/huj/dispap/dp512.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://ratio.huji.ac.il/sites/default/files/publications/dp512.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, April.
    2. 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.
    3. 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.
    4. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206, October.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636, October.
    5. MERTENS, Jean-François & ZAMIR, Shmuel, 1977. "The maximal variation of a bounded martingale," LIDAM Reprints CORE 309, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. 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.
    7. MERTENS, Jean-François & ZAMIR, Shmuel, 1971. "The value of two-person zero-sum repeated games with lack of information on both sides," LIDAM Reprints CORE 154, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Laraki, Rida & Sorin, Sylvain, 2015. "Advances in Zero-Sum Dynamic Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    3. VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," HEC Research Papers Series 754, HEC Paris.
    4. Rida Laraki, 2010. "Explicit formulas for repeated games with absorbing states," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 53-69, March.
    5. Vieille, Nicolas, 2002. "Stochastic games: Recent results," 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 48, pages 1833-1850, Elsevier.
    6. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 172-207, March.
    7. Fedor Sandomirskiy, 2018. "On Repeated Zero-Sum Games with Incomplete Information and Asymptotically Bounded Values," Dynamic Games and Applications, Springer, vol. 8(1), pages 180-198, March.
    8. Pierre Cardaliaguet & Rida Laraki & Sylvain Sorin, 2012. "A Continuous Time Approach for the Asymptotic Value in Two-Person Zero-Sum Repeated Games," Post-Print hal-00609476, HAL.
    9. Laraki, Rida & Renault, Jérôme, 2017. "Acyclic Gambling Games," TSE Working Papers 17-768, Toulouse School of Economics (TSE).
    10. Shmaya, Eran & Solan, Eilon, 2004. "Zero-sum dynamic games and a stochastic variation of Ramsey's theorem," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 319-329, August.
    11. Abraham Neyman, 2013. "The Maximal Variation of Martingales of Probabilities and Repeated Games with Incomplete Information," Journal of Theoretical Probability, Springer, vol. 26(2), pages 557-567, June.
    12. A. Souquière, 2010. "Approximation and representation of the value for some differential games with asymmetric information," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 699-722, October.
    13. Fedor Sandomirskiy, 2014. "Repeated games of incomplete information with large sets of states," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 767-789, November.
    14. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
    15. Koessler, Frederic & Laclau, Marie & Renault, Jérôme & Tomala, Tristan, 2022. "Long information design," Theoretical Economics, Econometric Society, vol. 17(2), May.
    16. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "The MaxMin value of stochastic games with imperfect monitoring," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(1), pages 133-150, December.
    17. Ehud Lehrer & Dinah Rosenberg, 2003. "Information and Its Value in Zero-Sum Repeated Games," Game Theory and Information 0312003, University Library of Munich, Germany.
    18. Salomon, Antoine & Forges, Françoise, 2015. "Bayesian repeated games and reputation," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 70-104.
    19. Shmuel Zamir, 2008. "Bayesian games: Games with incomplete information," Discussion Paper Series dp486, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    20. Neyman, Abraham, 2017. "Continuous-time stochastic games," Games and Economic Behavior, Elsevier, vol. 104(C), pages 92-130.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:huj:dispap:dp512. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Michael Simkin (email available below). General contact details of provider: https://edirc.repec.org/data/crihuil.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.