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

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Listed author(s):
  • 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/pii/S0899-8256(07)00157-1
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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
Contact details of provider: 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. Oyama, Daisuke & Takahashi, Satoru & Hofbauer, Josef, 2008. "Monotone methods for equilibrium selection under perfect foresight dynamics," Theoretical Economics, Econometric Society, vol. 3(2), June.
  3. Frankel, David M. & Morris, Stephen & Pauzner, Ady, 2003. "Equilibrium selection in global games with strategic complementarities," Journal of Economic Theory, Elsevier, vol. 108(1), pages 1-44, January.
  4. 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.
  5. 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.
  6. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
  7. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
  8. Roberts, David P., 2005. "Pure Nash equilibria of coordination matrix games," Economics Letters, Elsevier, vol. 89(1), pages 7-11, October.
  9. 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.
  10. 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.
  11. Powers, Imelda Yeung, 1990. "Limiting Distributions of the Number of Pure Strategy Nash Equilibria in N-Person Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(3), pages 277-286.
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Cited by:

  1. Laurent Mathevet, 2010. "A contraction principle for finite global games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(3), pages 539-563, March.
  2. Arieli, Itai & Babichenko, Yakov, 2016. "Random extensive form games," Journal of Economic Theory, Elsevier, vol. 166(C), pages 517-535.

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