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Stochastic games with a single controller and incomplete information

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  • VIEILLE, Nicolas

    ()

  • ROSENBERG, Dinah

    ()

  • SOLAN, Eilon

    ()

Abstract

We study stochastic games with incomplete information on one side, where the transition is controlled by one of the players. We prove that if the informed player also controls the transition, the game has a value, whereas if the uninformed player controls the transition, the max-min value, as well as the min-max value, exist, but they may differ. We discuss extensions to the case of incomplete information on both sides.

Suggested Citation

  • VIEILLE, Nicolas & ROSENBERG, Dinah & SOLAN, Eilon, 2002. "Stochastic games with a single controller and incomplete information," Les Cahiers de Recherche 754, HEC Paris.
  • Handle: RePEc:ebg:heccah:0754
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    References listed on IDEAS

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    1. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," CORE Discussion Papers 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, January.
    3. Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107662636.
      • Mertens,Jean-François & Sorin,Sylvain & Zamir,Shmuel, 2015. "Repeated Games," Cambridge Books, Cambridge University Press, number 9781107030206.
    4. Aumann, Robert J. & Heifetz, Aviad, 2002. "Incomplete information," 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 43, pages 1665-1686 Elsevier.
    5. 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.
    6. repec:dau:papers:123456789/6231 is not listed on IDEAS
    7. Nicolas Vieille & Dinah Rosenberg, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Post-Print hal-00481429, HAL.
    8. SORIN, Sylvain, 1985. ""Big match" with lack of information on one side (Part II)," CORE Discussion Papers RP 665, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. 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.
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    Citations

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    Cited by:

    1. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2002. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. 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.
    3. 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.
    4. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    More about this item

    Keywords

    stochastic games; zero-sum games; incomplete information; value; maxmin;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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