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
SN - 0377-2217
VL - 252
SP - 213
EP - 219
JO - European Journal of Operational Research
JF - European Journal of Operational Research
IS - 1
ER -