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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. Echenique, Federico, 2004. "A characterization of strategic complementarities," Games and Economic Behavior, Elsevier, vol. 46(2), pages 325-347, February.
  4. 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.
  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. 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.
  7. 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.
  8. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
  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;Game Theory Society, vol. 19(3), pages 277-286.
  10. 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.
  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;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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