A Computational Study of Interval-Valued Matrix Games

Abstract

Game theory has been applied for strategic decision making in areas such as economics, political science, psychology, and others. A two-player zero-sum game represented as an m × n real matrix is probably the simplest model to maximize (minimize) possible gain (loss) in game theory. Considering payoffs of a matrix game in real applications can vary even when the players repeat the same strategies, Collins and Hu [1] modeled such uncertainty with interval-valued matrix games. In 2011 and 2012, D.F. Li et al further proposed approaches to solve interval-valued matrix game with the basic idea of splitting an interval game matrix to its lower and upper bounds in [5] and [6]. It is also suggested that one may determine an interval matrix game by solving the lower-and upper-bound point matrix games. However, there is not a rigorous mathematical proof but only few structured numerical examples were used for verification. In this study, we run exhaustive computational experiments with the software suite we created to gain further insights. Our computational results indicate that the value of a point-valued matrix game R ∈ R, where R is an interval-valued matrix game, is bounded by the game values of the lower- and upper-bound point matrix of R mostly. However, it is not always true. We report the software suite, our results of computational experiments, and theoretic insights in this paper.