A Novel Algorithm For Finding Equilibrium Strategy In Two Person Zero Sum Game With Fuzzy Strategy Sets And Payoffs

Abstract

This paper investigates a two person zero sum matrix game in which the payoffs and strategy are characterized as random fuzzy variables. Using the operations of triangular fuzzy numbers, the fuzzy payoffs for all synthetic outcomes are calculated. Based on random fuzzy expected value operator, a random fuzzy expected minimax equilibrium strategy to the game is defined. After that, based on the constraints, the feasible strategy string sets of the players for multi conflict situations are constructed. Then an iterative algorithm based on random fuzzy simulation is designed to seek the minimax equilibrium strategy. Using a linear ranking function, the aggregation model can be solved by transforming it into a crisp bimatrix game. Then, the fuzzy synthetic aggregation model is established and solved by transforming it into a crisp bimatrix game. Finally, a military example is provided to illustrate the practicality and effectively of the model.