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Stochastic Games with a Single Controller and Incomplete Information

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  • Dinah Rosenberg
  • Eilon Solan
  • Nicolas Vieille

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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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1346.

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Date of creation: May 2002
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Handle: RePEc:nwu:cmsems:1346

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  1. 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.
  2. 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).
  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. Rosenberg, Dinah & Vieille, Nicolas, 2000. "The Maxmin of Recursive Games with Incomplete Information on one Side," Economics Papers from University Paris Dauphine 123456789/6231, Paris Dauphine University.
  5. Robert J. Aumann, 1995. "Repeated Games with Incomplete Information," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262011476, December.
  6. Mertens, J.-F., 1986. "Repeated games," CORE Discussion Papers 1986024, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Aumann, Robert J. & Heifetz, Aviad, 2001. "Incomplete Information," Working Papers 1124, California Institute of Technology, Division of the Humanities and Social Sciences.
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Cited by:
  1. Abraham Neyman, 2002. "Stochastic games: Existence of the MinMax," Discussion Paper Series dp295, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. Dinah Rosenberg & Eilon Solan & Nicolas Vieille, 2003. "Stochastic Games with Imperfect Monitoring," Discussion Papers 1376, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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.

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