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Distribution of pure Nash equilibria in n-person games with random best replies

  • Klaus Kultti
  • Hannu Salonen
  • Hannu Vartiainen

    ()

In this paper we study the number of pure strategy Nash equilibria in large finite n-player games. A distinguishing feature of our study is that we allow general - potentially multivalued - best reply correspondences. Given the number K of pure strategies to each player, we assign to each player a distribution over the number of his pure best replies against each strategy profile of his opponents. If the means of these distributions have a limit (mu)i for each player i as the number K of pure strategies goes to infinity, then the limit number of pure equilibria is Poisson distributed with a mean equal to the product of the limit means (mu)i. In the special case when all best reply mappings are equally likely, the probability of at least one pure Nash equilibrium approaches one and the expected number of pure Nash equilibria goes to infinity.

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Paper provided by Aboa Centre for Economics in its series Discussion Papers with number 71.

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Length: 21
Date of creation: Dec 2011
Date of revision:
Handle: RePEc:tkk:dpaper:dp71
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  1. Sophie Bade & Guillaume Haeringer & Ludovic Renou, 2005. "More Strategies, More Nash Equilibria," School of Economics Working Papers 2005-01, University of Adelaide, School of Economics.
  2. 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.
  3. 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.
  4. 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.
  5. Andrew McLennan, 2005. "The Expected Number of Nash Equilibria of a Normal Form Game," Econometrica, Econometric Society, vol. 73(1), pages 141-174, 01.
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