Chance-constrained games with mixture distributions

Shen Peng (), Navnit Yadav (), Abdel Lisser () and Vikas Vikram Singh ()
Additional contact information
Shen Peng: KTH Royal Institute of Technology
Navnit Yadav: Indian Institute of Technology Delhi
Abdel Lisser: L2S, CentraleSupélec Bât Breguet A4.22 3 rue Joliot Curie
Vikas Vikram Singh: Indian Institute of Technology Delhi

Mathematical Methods of Operations Research, 2021, vol. 94, issue 1, No 3, 97 pages

Abstract: Abstract In this paper, we consider an n-player non-cooperative game where the random payoff function of each player is defined by its expected value and her strategy set is defined by a joint chance constraint. The random constraint vectors are independent. We consider the case when the probability distribution of each random constraint vector belongs to a subset of elliptical distributions as well as the case when it is a finite mixture of the probability distributions from the subset. We propose a convex reformulation of the joint chance constraint of each player and derive the bounds for players’ confidence levels and the weights used in the mixture distributions. Under mild conditions on the players’ payoff functions, we show that there exists a Nash equilibrium of the game when the players’ confidence levels and the weights used in the mixture distributions are within the derived bounds. As an application of these games, we consider the competition between two investment firms on the same set of portfolios. We use a best response algorithm to compute the Nash equilibria of the randomly generated games of different sizes.

Keywords: Chance-constrained game; Mixture of elliptical distributions; Nash equilibrium; Portfolio (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-021-00747-9

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