Home // International Journal On Advances in Systems and Measurements, volume 15, numbers 3 and 4, 2022 // View article
Authors:
Nguyen Hoang Nam
Vikas Vikram Singh
Abdel Lisser
Monika Arora
Keywords: Distributionally robust chance constraints; Zero-sum game; Saddle point equilibrium; Second-order cone program
Abstract:
We consider a two-player zero-sum game with random linear chance constraints whose distributions are known to belong to moments based uncertainty sets or statistical distance based uncertainty sets. The game with chance constraints can be used in various applications, e.g., risk constraints in portfolio optimization, resource constraints in stochastic shortest path problem, renewable energy aggregators in the local market. We propose a reformulation of the chance constraints using distributionally chance-constrained optimization framework. We show that there exists a saddle point equilibrium of the game, which is the optimal solution of a primal-dual pair of second-order cone programs. As an application, we present a competition of two firms in financial market to simulate our theoretical results.
Pages: 107 to 120
Copyright: Copyright (c) to authors, 2022. Used with permission.
Publication date: December 31, 2022
Published in: journal
ISSN: 1942-261x