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

Jianqiang Cheng, Janny Leung, Abdel Lisser

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)213-219
Number of pages7
JournalEuropean Journal of Operational Research
Volume252
Issue number1
DOIs
StatePublished - Jul 1 2016
Externally publishedYes

Keywords

  • Joint probabilistic constraints
  • Random payoff
  • Second-order cone programming
  • Stochastic programming
  • Two-person zero-sum game

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

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