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Vikas Vikram Singh(vikassinghiitd.ac.in) Abstract: We consider an nplayer noncooperative game with random payoffs and continuous strategy set for each player. The random payoffs of each player are defined using a finite dimensional random vector. We formulate this problem as a chanceconstrained game by defining the payoff function of each player using a chance constraint. We first consider the case where the continuous strategy set of each player does not depend on the strategies of other players. If a random vector defining the payoffs of each player follows a multivariate elliptically symmetric distribution, we show that there exists a Nash equilibrium. We characterize the set of Nash equilibria using the solution set of a variational inequality (VI) problem. Next, we consider the case where the continuous strategy set of each player is defined by a shared constraint set. In this case, we show that there exists a generalized Nash equilibrium for elliptically symmetric distributed payoffs. Under certain conditions, we characterize the set of a generalized Nash equilibria using the solution set of a VI problem. As an application, the random payoff games arising from electricity market are studied under chanceconstrained game framework. Keywords: Chanceconstrained games · Variational Inequality · Elliptically symmetric distribution · Generalized Nash equilibrium · Cournot competition. Category 1: Stochastic Programming Category 2: Other Topics (Game Theory ) Citation: Download: [PDF] Entry Submitted: 11/24/2017 Modify/Update this entry  
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