Simple search methods for finding a Nash equilibrium
AbstractWe 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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Bibliographic InfoArticle provided by Elsevier in its journal Games and Economic Behavior.
Volume (Year): 63 (2008)
Issue (Month): 2 (July)
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Web page: http://www.elsevier.com/locate/inca/622836
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- C. E. Lemke, 1965. "Bimatrix Equilibrium Points and Mathematical Programming," Management Science, INFORMS, vol. 11(7), pages 681-689, May.
- 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.
- 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, 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, 1994. "The Maximal Number of Regular Totally Mixed Nash Equilibria," Working Papers 865, California Institute of Technology, Division of the Humanities and Social Sciences.
- E. Kohlberg & J.-F. Mertens, 1998.
"On the Strategic Stability of Equilibria,"
Levine's Working Paper Archive
445, David K. Levine.
- 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.
- Itzhak Gilboa & Eitan Zemel, 1988.
"Nash and Correlated Equilibria: Some Complexity Considerations,"
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Andrew McLennan & Rabee Tourky, 2008.
"Imitation Games and Computation,"
Discussion Papers Series
359, School of Economics, University of Queensland, Australia.
- 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.
- Conitzer, Vincent & Sandholm, Tuomas, 2008. "New complexity results about Nash equilibria," Games and Economic Behavior, Elsevier, vol. 63(2), pages 621-641, July.
- Ruchira Datta, 2010. "Finding all Nash equilibria of a finite game using polynomial algebra," Economic Theory, Springer, vol. 42(1), pages 55-96, January.
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