Nash equilibria of Cauchy-random zero-sum and coordination matrix games

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We consider zero-sum games (A, -A) and coordination games (A,A), where A is an m-by-n matrix with entries chosen independently with respect to the Cauchy distribution. In each case, we give an exact formula for the expected number of Nash equilibria with a given support size and payoffs in a given range, and also asymptotic simplications for matrices of a fixed shape and increasing size. We carefully compare our results with recent results of McLennan and Berg on Gaussian random bimatrix games (A,B), and describe how the three situations together shed light on random bimatrix games in general.

Original languageEnglish (US)
Pages (from-to)167-184
Number of pages18
JournalInternational Journal of Game Theory
Issue number2
StatePublished - Jul 2006


  • Cauchy distribution
  • Coordination game
  • Nash equilibrium
  • Support size
  • Zero-sum game


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