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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.

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Bibliographic Info

Paper provided by HEC Paris in its series Les Cahiers de Recherche with number 754.

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Length: 23 pages
Date of creation: 03 May 2002
Date of revision:
Handle: RePEc:ebg:heccah:0754

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

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References

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  1. Zamir, Shmuel, 1992. "Repeated games of incomplete information: Zero-sum," Handbook of Game Theory with Economic Applications, Elsevier, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 5, pages 109-154 Elsevier.
  2. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262011476, December.
  3. Rosenberg, Dinah & Vieille, Nicolas, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/6231, Paris Dauphine University.
  4. DE MEYER , Bernard, 1993. "Repeated Games and the Central Limit Theorem," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1993003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers, California Institute of Technology, Division of the Humanities and Social Sciences 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
  6. MERTENS, Jean-François, . "Stochastic games," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1587, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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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, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1341, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. Sylvain Sorin, 2011. "Zero-Sum Repeated Games: Recent Advances and New Links with Differential Games," Dynamic Games and Applications, Springer, Springer, vol. 1(1), pages 172-207, March.
  3. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series, The Center for the Study of Rationality, Hebrew University, Jerusalem dp295, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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