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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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File URL: http://www.sciencedirect.com/science/article/B6WFW-4R29FM9-1/1/e8f810ddf47745e8a3ab7dc0b1140ecb
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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. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium Selection in Global Games with Strategic Complementarities," Staff General Research Papers 11920, Iowa State University, Department of Economics.
  2. 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.
  3. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
  4. Federico Echenique, 2001. "A characterization of strategic complementarities," Documentos de Trabajo (working papers) 0501, Department of Economics - dECON.
  5. Echenique, Federico & Edlin, Aaron S., 2004. "Mixed equilibria are unstable in games of strategic complements," Berkeley Olin Program in Law & Economics, Working Paper Series qt1ht651hk, Berkeley Olin Program in Law & Economics.
  6. 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.
  7. 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.
  8. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
  9. 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.
  10. Roberts, David P., 2005. "Pure Nash equilibria of coordination matrix games," Economics Letters, Elsevier, vol. 89(1), pages 7-11, October.
  11. 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.
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Cited by:
  1. Mathevet, Laurent, . "A contraction principle for finite global games," Working Papers 1243, California Institute of Technology, Division of the Humanities and Social Sciences.

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