Solving constrained matrix games with fuzzy random linear constraints

Abstract

In real-world games, players may face an uncertain environment where fuzziness and randomness coexist. The main difficulty in dealing with games involving fuzziness and randomness arises when comparing the payoffs. The purpose of this paper is to introduce a new approach to deal with constrained matrix games where the entries of the constraint matrices are LR-fuzzy random variables. Our methodology is based on constructing a new matrix game using the chance constraint method adapted to the probability-possibility measures. First, a specific type of saddle point is defined as an equilibrium solution. Then, conditions for the existence of the proposed solution are established. Further, a technique based on second-order programming for computing the saddle point is presented. Finally, a numerical illustration of the approach is provided.