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On Games of Perfect Information: Equilibria, E-Equilibria and Approximation by Simple Games

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  • Carmona, Guilherme

Abstract

We show that every bounded, continuous at infinity game of perfect information has an "!perfect equilibrium. Our method consists of approximating the payoff function of each player by a sequence of simple functions, and to consider the corresponding sequence of games, each differing form the original game only on the payoff function. In addition, this approach yields a new characterization of perfect equilibria: a strategy f is a perfect equilibrium in such a game G if and only if it is an 1=n!perfect equilibrium in Gn for all n, where fGng stand for our approximation sequence.

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  • Carmona, Guilherme, 2003. "On Games of Perfect Information: Equilibria, E-Equilibria and Approximation by Simple Games," FEUNL Working Paper Series wp427, Universidade Nova de Lisboa, Faculdade de Economia.
  • Handle: RePEc:unl:unlfep:wp427
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    References listed on IDEAS

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    1. Drew Fudenberg & David Levine, 2008. "Limit Games and Limit Equilibria," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 2, pages 21-39 World Scientific Publishing Co. Pte. Ltd..
    2. Borgers, Tilman, 1991. "Upper hemicontinuity of the correspondence of subgame-perfect equilibrium outcomes," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 89-106.
    3. Borgers, Tilman, 1989. "Perfect equilibrium histories of finite and infinite horizon games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 218-227, February.
    4. Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
    5. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters,in: A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20 World Scientific Publishing Co. Pte. Ltd..
    6. Christopher Harris & John Vickers, 1985. "Perfect Equilibrium in a Model of a Race," Review of Economic Studies, Oxford University Press, vol. 52(2), pages 193-209.
    7. Hellwig, Martin & Leininger, Wolfgang & Reny, Philip J. & Robson, Arthur J., 1990. "Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games," Journal of Economic Theory, Elsevier, vol. 52(2), pages 406-422, December.
    8. Harris, Christopher J, 1985. "Existence and Characterization of Perfect Equilibrium in Games of Perfect Information," Econometrica, Econometric Society, vol. 53(3), pages 613-628, May.
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    Cited by:

    1. Hannu Salonen & Hannu Vartiainen, 2011. "On the Existence of Markov Perfect Equilibria in Perfect Information Games," Discussion Papers 68, Aboa Centre for Economics.

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