The two-person and zero-sum matrix game with probabilistic linguistic information

Abstract

Game theory establishes mathematical models of strategic interactions among rational decision-makers. In many situations, the crisp values of payoffs are difficult to obtain while the probabilistic linguistic information is easy to collect. However, the existing research on matrix game did not consider the probabilistic linguistic information. To bridge this gap, this study takes the probabilistic linguistic information as the input of a two-person and zero-sum matrix game, and addresses the vague information by triangular membership functions. Such a two-person and zero-sum matrix game with probabilistic linguistic information is a useful technique for multiple criteria analysis. In addition, it outputs the same form of information as the inputs to increase the interpretability compared with other uncertain matrix games. An illustrative example about the forest management is provided to show the validity and advantages of the two-person and zero-sum matrix game with probabilistic linguistic information.