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Finding a Nash Equilibrium in Spatial Games is an NP-Complete Problem

Author

Listed:
  • Richard Baron

    (CREUSET, University of Saint-Etienne)

  • Jaçques Durieu

    (CREUSET, University of Saint-Etienne)

  • Hans Haller

    (Virginia Polytechnic Institute and State University)

  • Philippe Solal

    (CREUSET, University of Saint-Etienne)

Abstract

We consider the class of (finite) spatial games. We show that the problem of determining whether there exists a Nash equilibrium in which each player has a payoff of at least k is NP-complete as a function of the number of players. When each player has two strategies and the base game is an anti-coordination game, the problem is decidable in polynomial time.

Suggested Citation

  • Richard Baron & Jaçques Durieu & Hans Haller & Philippe Solal, 2002. "Finding a Nash Equilibrium in Spatial Games is an NP-Complete Problem," Discussion Papers 02-19, University of Copenhagen. Department of Economics, revised Nov 2002.
    • Handle: RePEc:kud:kuiedp:0219
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    File URL: http://www.econ.ku.dk/english/research/publications/wp/2002/0219.pdf/
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    Cited by:

    1. Demuynck, Thomas, 2011. "The computational complexity of rationalizing boundedly rational choice behavior," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 425-433.
    2. R. S. Bartholo & C. A. Cosenza & F. A. Doria & M. Doria & A. Teixeira, 2011. "On Exact and Approximate Solutions for Hard Problems: An Alternative Look," ASSRU Discussion Papers 1103, ASSRU - Algorithmic Social Science Research Unit.

    More about this item

    Keywords

    spatial games; NP-completeness; graph K-colorability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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