A Characterization of Nash Equilibrium for the Games with Random Payoffs

Vikas Vikram Singh () and Abdel Lisser ()
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Vikas Vikram Singh: Indian Institute of Technology Delhi
Abdel Lisser: Université Paris Sud

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 14, 998-1013

Abstract: Abstract We consider a two-player random bimatrix game where each player is interested in the payoffs which can be obtained with certain confidence. The payoff function of each player is defined using a chance constraint. We consider the case where the entries of the random payoff matrix of each player jointly follow a multivariate elliptically symmetric distribution. We show an equivalence between the Nash equilibrium problem and the global maximization of a certain mathematical program. The case where the entries of the payoff matrices are independent normal/Cauchy random variables is also considered. The case of independent normally distributed random payoffs can be viewed as a special case of a multivariate elliptically symmetric distributed random payoffs. As for Cauchy distribution, we show that the Nash equilibrium problem is equivalent to the global maximization of a certain quadratic program. Our theoretical results are illustrated by considering randomly generated instances of the game.

Keywords: Chance-constrained games; Nash equilibrium; Elliptically symmetric distribution; Cauchy distribution; Mathematical program; Quadratic program; 91A10; 90C15; 90C20; 90C26 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-018-1343-0

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