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 traditional real-valued case. This game is called as an interval matrix game and its characterization of 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 parameter, which takes the evaluation of the given interval. Numerical examples are given to illustrate our idea. These results are applied to the fuzzy matrix game and the zero-sum interval stochastic game. Also an extension to a stochastic game with fuzzy payoff are considered.