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Fictitious play in `one-against-all' multi-player games

Author

Listed:
  • Aner Sela

    (Department of Economics, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva 84105, ISRAEL)

Abstract

A compound game is an (n + 1) player game based on n two-person subgames. In each of these subgames player 0 plays against one of the other players. Player 0 is regulated, so that he must choose the same strategy in all n subgames. We show that every fictitious play process approaches the set of equilibria in compound games for which all subgames are either zero-sum games, potential games, or $2\times 2$ games.

Suggested Citation

  • Aner Sela, 1999. "Fictitious play in `one-against-all' multi-player games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 635-651.
    • Handle: RePEc:spr:joecth:v:14:y:1999:i:3:p:635-651
    Note: Received: July 18, 1997; revised version: December 4, 1998
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    Citations

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    Cited by:

    1. Morris, Stephen & Ui, Takashi, 2004. "Best response equivalence," Games and Economic Behavior, Elsevier, vol. 49(2), pages 260-287, November.
    2. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    3. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    4. Ulrich Berger, 2003. "Fictitious play in 2xn games," Game Theory and Information 0303009, University Library of Munich, Germany.

    More about this item

    Keywords

    Learning; Fictitious play; Zero-sum games; Potential games.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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