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

Listed author(s):
  • Guilherme Carmona

We show that every bounded, continuous at infinity game of perfect information has an epsilon-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 G_n for all n, where {G_n} stand for our approximation sequence.

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File URL: http://econwpa.repec.org/eps/game/papers/0402/0402002.pdf
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Paper provided by EconWPA in its series Game Theory and Information with number 0402002.

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Length: 20 pages
Date of creation: 09 Feb 2004
Handle: RePEc:wpa:wuwpga:0402002
Note: Type of Document - pdf; prepared on winxp; to print on general; pages: 20; figures: 0. none
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Fudenberg, Drew & Levine, David, 1986. "Limit games and limit equilibria," Journal of Economic Theory, Elsevier, vol. 38(2), pages 261-279, April.
  2. 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.
  3. Borgers, Tilman, 1991. "Upper hemicontinuity of the correspondence of subgame-perfect equilibrium outcomes," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 89-106.
  4. 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.
  5. Fudenberg, Drew & Levine, David, 1983. "Subgame-perfect equilibria of finite- and infinite-horizon games," Journal of Economic Theory, Elsevier, vol. 31(2), pages 251-268, December.
  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. Borgers, Tilman, 1989. "Perfect equilibrium histories of finite and infinite horizon games," Journal of Economic Theory, Elsevier, vol. 47(1), pages 218-227, February.
  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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