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Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium

Vikas Vikram Singh (vikas.singh***at***lri.fr)
Oualid Jouini (oualid.jouini***at***ecp.fr)
Abdel Lisser (lisser***at***lri.fr)

Abstract: We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider two types of distributional uncertainty sets. We show the existence of a mixed strategy Nash equilibrium of a distributionally robust chance-constrained game corresponding to both types of distributional uncertainty sets. For each case, we show a one-to-one correspondence between a Nash equilibrium of a game and a global maximum of a certain mathematical program.

Keywords: Distributionally robust chance-constrained games, Chance-constraints, Nash equilibrium, Semidefinite programming, Mathematical program

Category 1: Stochastic Programming

Category 2: Other Topics (Game Theory )

Citation:

Download: [PDF]

Entry Submitted: 09/25/2015
Entry Accepted: 09/25/2015
Entry Last Modified: 04/02/2016

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