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A family of identities related to zero-sum and team games

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  • Stanford, William

Abstract

We list and prove a family of binomial identities by calculating in two ways the probabilities of approximate saddlepoints occurring in random mxn matrices. The identities are easily seen to be equivalent to the evaluation of a family of Gauss 2F1 polynomials according to a formula of Vandermonde. We also consider some implications concerning the number of approximate pure strategy Nash equilibria we can expect in large matrix zero-sum and team games.

Suggested Citation

  • Stanford, William, 2011. "A family of identities related to zero-sum and team games," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 91-94, September.
    • Handle: RePEc:eee:matsoc:v:62:y:2011:i:2:p:91-94
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    References listed on IDEAS

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    1. Stanford, William, 2004. "Individually rational pure strategies in large games," Games and Economic Behavior, Elsevier, vol. 47(1), pages 221-233, April.
    2. Ehud Kalai, 2004. "Large Robust Games," Econometrica, Econometric Society, vol. 72(6), pages 1631-1665, November.
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