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Games with distributionally robust joint chance constraints

Shen Peng (shenp***at***kth.se)
Abdel Lisser (abdel.lisser***at***lri.fr)
Vikas Vikram Singh (vikassingh***at***maths.iitd.ac.in)
Nalin Gupta (nalingupta98***at***gmail.com)
Eshan Balachandar (eshan.balachandar***at***gmail.com)

Abstract: This paper studies an n-player non-cooperative game with strategy sets defined by stochastic linear constraints. The stochastic constraints of each player are jointly satisfied with a probability exceeding a given threshold. 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 random constraints of each player are formulated as a distributionally robust joint chance constraint. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty set is based on a nonnegative support. Under standard assumptions on players' payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set.

Keywords: Chance-constrained game, Nash equilibrium, Distributionally robust optimization, Nonnegative support.

Category 1: Stochastic Programming

Category 2: Other Topics (Game Theory )


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Entry Submitted: 01/16/2020
Entry Accepted: 01/16/2020
Entry Last Modified: 11/10/2020

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