Existence of Nash equilibrium for chance-constrained games

Singh, Vikas; Jouini, Oualid; Lisser, Abdel

doi:10.1016/j.orl.2016.07.013

Cited by 33 publications

(21 citation statements)

References 18 publications

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“…Motivated by recent research on robust game theory and distributinally robust finite game [1,36,31,32,2,41], we study several distributionally robust equilibrium models. We start with a distributionally robust Nash equilibrium (DRNE) model.…”

Section: Resultsmentioning

confidence: 99%

“…Ahipasaoglu et al [2] study the DRO stochastic user equilibrium where the players only have the information of the first and second moments of the random variables. Singh et al [41] consider robust finite chance-constrained games and study the existence of mixed-strategy Nash equilibrium. Along that direction, Loizou [31,32] proposes a distributionally robust Nash equilibirum model with each player's objective being Conditional Value at Risk (CVaR for short).…”

Section: Introductionmentioning

confidence: 99%

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Distributionally robust equilibrium for continuous games: Nash and Stackelberg models

Liu

Yang

et al. 2018

European Journal of Operational Research

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributionally robust equilibrium for continuous games: Nash and Stackelberg models

Liu

Yang

et al. 2018

European Journal of Operational Research

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“…For the uncertainties involving random variables, the expected payoff criterion is used in case of risk neutral players [15,16,19,26,35,36] and the risk measures CVaR and variance are used in the risk averse case [10,18,26]. For finite strategic games with random payoffs, Singh et al [29,30,31] introduced a chance constraint programming based payoff criterion. It captures a situation where players are guaranteed to get the payoffs with a certain confidence level.…”

Section: Introductionmentioning

confidence: 99%

“…It captures a situation where players are guaranteed to get the payoffs with a certain confidence level. There exists a mixed strategy Nash equilibrium of a chance-constrained game if the payoff vector of each player follows a multivariate elliptically symmetric distribution [29]. Such a Nash equilibrium can be computed by solving an equivalent mathematical program [31].…”

Section: Introductionmentioning

confidence: 99%

Games with distributionally robust joint chance constraints

et al. 2021

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This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chanceconstrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players' payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.

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“…For risk averse players, the payoff criterion with the risk measure CVaR [14,20] and the variance was considered in the literature [6]. Singh et al [22,24] considered a finite strategic game where the payoff vector of each player is a random vector.…”

Section: Introductionmentioning

confidence: 99%