Variational inequality formulation 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 Global Optimization, 2018, vol. 72, issue 4, No 7, 743-760

Abstract: 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; 91A10; 90C15; 90C33 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10898-018-0664-8

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