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The number of pure Nash equilibria in a random game with nondecreasing best responses

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  • Takahashi, Satoru

Abstract

We randomly draw a game from a distribution on the set of two-player games with a given size. We compute the distribution and the expectation of the number of pure-strategy Nash equilibria of the game conditional on the game having nondecreasing best-response functions. The conditional expected number of pure-strategy Nash equilibria becomes much larger than the unconditional expected number as the size of the game grows.

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Bibliographic Info

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

Volume (Year): 63 (2008)
Issue (Month): 1 (May)
Pages: 328-340

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Handle: RePEc:eee:gamebe:v:63:y:2008:i:1:p:328-340

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

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  1. Josef Hofbauer & Daisuke Oyama & Satoru Takahashi, 2004. "Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics," Econometric Society 2004 North American Winter Meetings 339, Econometric Society.
  2. Echenique, Federico, 2001. "A Characterization of Strategic Complementarities," Department of Economics, Working Paper Series qt5w13s4z2, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  3. David M. Frankel & Stephen Morris & Ady Pauzner, 2000. "Equilibrium Selection in Global Games with Strategic Complementarities," Econometric Society World Congress 2000 Contributed Papers 1490, Econometric Society.
  4. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer, vol. 19(3), pages 277-86.
  5. Stanford, William, 1999. "On the number of pure strategy Nash equilibria in finite common payoffs games," Economics Letters, Elsevier, vol. 62(1), pages 29-34, January.
  6. Echenique, Federico & Edlin, Aaron, 2004. "Mixed equilibria are unstable in games of strategic complements," Journal of Economic Theory, Elsevier, vol. 118(1), pages 61-79, September.
  7. McLennan, A., 1999. "The Expected Number of Nash Equilibria of a Normal Form Game," Papers 306, Minnesota - Center for Economic Research.
  8. 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.
  9. 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.
  10. Stanford, William, 1997. "On the distribution of pure strategy equilibria in finite games with vector payoffs," Mathematical Social Sciences, Elsevier, vol. 33(2), pages 115-127, April.
  11. Roberts, David P., 2005. "Pure Nash equilibria of coordination matrix games," Economics Letters, Elsevier, vol. 89(1), pages 7-11, October.
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Cited by:
  1. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer, vol. 42(3), pages 539-563, March.

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