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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.

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File URL: http://www.sciencedirect.com/science/article/B6WFW-4KPP4CR-1/1/d486446ac9548e421ae894e8dfbe9ff1
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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 63 (2008)
Issue (Month): 2 (July)
Pages: 642-662

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Handle: RePEc:eee:gamebe:v:63:y:2008:i:2:p:642-662

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Web page: http://www.elsevier.com/locate/inca/622836

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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.
2. C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
3. Von Stengel, Bernhard, 2002. "Computing equilibria for two-person games," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 45, pages 1723-1759 Elsevier.
4. Itzhak Gilboa & Eitan Zemel, 1988. "Nash and Correlated Equilibria: Some Complexity Considerations," Discussion Papers 777, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
   
   • Gilboa, Itzhak & Zemel, Eitan, 1989. "Nash and correlated equilibria: Some complexity considerations," Games and Economic Behavior, Elsevier, vol. 1(1), pages 80-93, March.
5. 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.
6. 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.
7. McKelvey, R.D. & McLennan, A., 1994. "The Maximal Number of Regular Totaly Mixed Nash Equilibria," Papers 272, Minnesota - Center for Economic Research.
   
   • 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.
   • McKelvey, Richard D. & McLennan, Andrew, 1994. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Working Papers 865, California Institute of Technology, Division of the Humanities and Social Sciences.
8. 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.
9. E. Kohlberg & J.-F. Mertens, 1998. "On the Strategic Stability of Equilibria," Levine's Working Paper Archive 445, David K. Levine.
   
   • Kohlberg, Elon & Mertens, Jean-Francois, 1986. "On the Strategic Stability of Equilibria," Econometrica, Econometric Society, vol. 54(5), pages 1003-37, September.
10. Talman, A.J.J. & Laan, G. van der & Van der Heyden, L., 1987. "Variable dimension algorithms for solving the nonlinear complementarity problem on a product of unit simplices using general labelling," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153106, Tilburg University.

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Cited by:

1. Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
2. Andrew McLennan & Rabee Tourky, 2008. "Imitation Games and Computation," Discussion Papers Series 359, School of Economics, University of Queensland, Australia.
   
   • 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.

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