Solving matrix game with rough payoffs using genetic algorithm

Abstract

In this paper, we analyze a matrix game using a rough programming approach. The combination of a matrix game and a rough programming approach represents a new class defined as a rough matrix game. The pay-off elements are characterized by rough variables, and the uncertainties of the rough variables are measured using a measure known as trust. Based on this trust measure, we defined trust equilibrium strategies and a rough expected value. We derived a series of optimal solutions to a rough matrix game using a genetic algorithm. We present a numerical example that illustrates the effectiveness of our rough matrix game.