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Variational inequality formulation for the games with random payoffs

Vikas Vikram Singh(vikassingh***at***iitd.ac.in)
Abdel Lisser(abdel.lisser***at***lri.fr)

Abstract: We consider an n-player non-cooperative 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 chance-constrained 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 chance-constrained game framework.

Keywords: Chance-constrained games Variational Inequality Elliptically symmetric distribution Generalized Nash equilibrium Cournot competition.

Category 1: Stochastic Programming

Category 2: Other Topics (Game Theory )


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Entry Submitted: 11/24/2017
Entry Accepted: 11/24/2017
Entry Last Modified: 11/24/2017

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