TY - JOUR

T1 - Random-payoff two-person zero-sum game with joint chance constraints

AU - Cheng, Jianqiang

AU - Leung, Janny

AU - Lisser, Abdel

N1 - Funding Information:
This research benefited from the support of the “FMJH Program Gaspard Monge in optimization and operation research”, and from the support to this program from EDF. PGMO/IROE grant No. 2012-042H. We are grateful to the referees for their valuable comments and suggestions that helped to improve significantly our paper.
Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We study a two-person zero-sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability. We prove that for the general random-payoff zero-sum game there exists a "weak duality" between the two formulations, i.e., the optimal value of the minimizing player is an upper bound of the one of the maximizing player. Under certain assumptions, we show that there also exists a "strong duality" where their optimal values are equal. Moreover, we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed. Finally, numerical examples are given to illustrate the performances of the proposed approaches.

AB - We study a two-person zero-sum game where the payoff matrix entries are random and the constraints are satisfied jointly with a given probability. We prove that for the general random-payoff zero-sum game there exists a "weak duality" between the two formulations, i.e., the optimal value of the minimizing player is an upper bound of the one of the maximizing player. Under certain assumptions, we show that there also exists a "strong duality" where their optimal values are equal. Moreover, we develop two approximation methods to solve the game problem when the payoff matrix entries are independent and normally distributed. Finally, numerical examples are given to illustrate the performances of the proposed approaches.

KW - Joint probabilistic constraints

KW - Random payoff

KW - Second-order cone programming

KW - Stochastic programming

KW - Two-person zero-sum game

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U2 - 10.1016/j.ejor.2015.12.024

DO - 10.1016/j.ejor.2015.12.024

M3 - Article

AN - SCOPUS:84960337699

VL - 252

SP - 213

EP - 219

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 1

ER -