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A Game with No Bayesian Approximate Equilibria

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  • Ziv Hellman

Abstract

Simon (2003) presented an example of a 3-player Bayesian games with no Bayesian equilibria but it has been an open question whether or not there are games with no approximate Bayesian equilibria. We present an example of a Bayesian game with two players, two actions and a continuum of states that possesses no approximate Bayesian equilibria, thus resolving the question. As a side benefit we also have for the first time an an example of a 2-player Bayesian game with no Bayesian equilibria and an example of a strategic-form game with no approximate Nash equilibria. The construction makes use of techniques developed in an example by Y. Levy of a discounted stochastic game with no stationary equilibria.

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Paper provided by The Center for the Study of Rationality, Hebrew University, Jerusalem in its series Discussion Paper Series with number dp615.

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Length: 12 pages
Date of creation: Jul 2012
Date of revision:
Handle: RePEc:huj:dispap:dp615

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  1. Yehuda (John) Levy, 2012. "A Discounted Stochastic Game with No Stationary Nash Equilibrium," Discussion Paper Series dp596r, The Center for the Study of Rationality, Hebrew University, Jerusalem, revised May 2012.
  2. Radner, Roy, 1980. "Collusive behavior in noncooperative epsilon-equilibria of oligopolies with long but finite lives," Journal of Economic Theory, Elsevier, vol. 22(2), pages 136-154, April.
  3. John C Harsanyi, 1997. "Games with incomplete information played by "bayesian" players," Levine's Working Paper Archive 1175, David K. Levine.
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