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Simple search methods for finding a Nash equilibrium

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  • Porter, Ryan
  • Nudelman, Eugene
  • Shoham, Yoav

Abstract

We present two simple search methods for computing a sample Nash equilibrium in a normal-form game: one for 2-player games and one for n-player games. Both algorithms bias the search towards supports that are small and balanced, and employ a backtracking procedure to efficiently explore these supports. Making use of a new comprehensive testbed, we test these algorithms on many classes of games, and show that they perform well against the state of the art--the Lemke-Howson algorithm for 2-player games, and Simplicial Subdivision and Govindan-Wilson for n-player games.

Suggested Citation

  • Porter, Ryan & Nudelman, Eugene & Shoham, Yoav, 2008. "Simple search methods for finding a Nash equilibrium," Games and Economic Behavior, Elsevier, vol. 63(2), pages 642-662, July.
  • Handle: RePEc:eee:gamebe:v:63:y:2008:i:2:p:642-662
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    References listed on IDEAS

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    1. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
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    5. Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
    6. McLennan, Andrew & Berg, Johannes, 2005. "Asymptotic expected number of Nash equilibria of two-player normal form games," Games and Economic Behavior, Elsevier, vol. 51(2), pages 264-295, May.
    7. Govindan, Srihari & Wilson, Robert, 2003. "A global Newton method to compute Nash equilibria," Journal of Economic Theory, Elsevier, vol. 110(1), pages 65-86, May.
    8. McKelvey, Richard D. & McLennan, Andrew, 1997. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Journal of Economic Theory, Elsevier, vol. 72(2), pages 411-425, February.
    9. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics,in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier.
    10. Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-1037, September.
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    Cited by:

    1. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(1), pages 55-96, January.
    2. McLennan, Andrew & Tourky, Rabee, 2010. "Imitation games and computation," Games and Economic Behavior, Elsevier, vol. 70(1), pages 4-11, September.
    3. Jiang, Albert Xin & Leyton-Brown, Kevin & Bhat, Navin A.R., 2011. "Action-Graph Games," Games and Economic Behavior, Elsevier, vol. 71(1), pages 141-173, January.
    4. Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
    5. Thompson, David R.M. & Leyton-Brown, Kevin, 2017. "Computational analysis of perfect-information position auctions," Games and Economic Behavior, Elsevier, vol. 102(C), pages 583-623.
    6. repec:eee:apmaco:v:251:y:2015:i:c:p:442-452 is not listed on IDEAS
    7. Godinho, Pedro & Dias, Joana, 2013. "Two-player simultaneous location game: Preferential rights and overbidding," European Journal of Operational Research, Elsevier, vol. 229(3), pages 663-672.

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