Abstract
In this paper, we formulate the random bimatrix game as a chance-constrained game using chance constraint. We show that a Nash equilibrium problem, corresponding to independent normally distributed payoffs, is equivalent to a nonlinear complementarity problem. Further if the payoffs are also identically distributed, a strategy pair where each player’s strategy is the uniform distribution over his action set, is a Nash equilibrium. We show that a Nash equilibrium problem corresponding to independent Cauchy distributed payoffs, is equivalent to a linear complementarity problem.
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This research was supported by Fondation DIGITEO, SUN grant No. 2014-0822D.
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Singh, V.V., Jouini, O., Lisser, A. (2017). Solving Chance-Constrained Games Using Complementarity Problems. In: Vitoriano, B., Parlier, G. (eds) Operations Research and Enterprise Systems. ICORES 2016. Communications in Computer and Information Science, vol 695. Springer, Cham. https://doi.org/10.1007/978-3-319-53982-9_4
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DOI: https://doi.org/10.1007/978-3-319-53982-9_4
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