An Interval Matrix Game and Its Applications to Fuzzy Matrix Game and Interval Stochastic Game

摘要

In this paper we consider a matrix game with interval-valued payoffs, which is a generation of the tritonal real-valued case. This game is called as an interval matrix game and its characterization o saddle point is discussed. It is shown that saddle points for the interval matrix game are (simultaneous) equilibrium points defined by two non-zero sum games with a defined by two non-zero sum games with a parameter, which takes the evaluation of the given interval. Numerical examples are given to illustrate our ideal. These results are applied to the fuzzy matrix game and the zero-sum interval stochastic gamma. Also and extension to a stochastic game with fuzzy payoff are considered.