TWO PLAYER ZERO SUM FUZZY GAMES FOR PLAYERS WITH DIFFERENT RISK LEVELS

Abstract

Two-player zero sum games, or in short matrix games, are useful models in game theory that models total conflict between the players. Since it is unrealistic for players to know exact payoff values in advance, in recent years fuzzy logic is implemented into matrix games to model payoff matrices. Various solution methods have been proposed in literature for matrix games with fuzzy payoffs, in which the solutions of the game are mostly presented as mixed strategies that make the game optimal and their respective α-cut values. Players’ different risk levels have not been considered in these methods. However, in real life players’ risk levels may differ since importance of the game can change for each player. Therefore main purpose of this thesis is to provide a solution method for two-player zero sum games with fuzzy payoffs, that considers each player’s different risk levels. In the method, α - cut concept is used in order to model risk levels for players. Mixed strategies that give the optimal game value are found by solving the game for specific α values. The proposed model is implemented to a real world problem to show its applicability and use. In the problem important marketing activities are aimed to be determined for two types of online shopping sites in Turkey, to maximize their return. The problem is modeled as two-player zero (constant) sum game by considering shopping sites as players and their pre-determined store attributes as game strategies. Expert opinions are used to determine payoff values and the fuzzy payoff matrix is created by converting linguistic expert data into triangular fuzzy numbers. Different risk levels are utilized in the problem since the importance of the game tend to be different for each e-store due to competitive environment. The solution of the game is found by the proposed model. Important marketing attributes for these two online store types are presented and discussed in terms of Turkish customers’ online shopping behavior and strategy definitions. The proposed model is found superior to the models proposed in the previous literature on matrix games with fuzzy payoffs, in terms of performance and computational easiness when players’ different risk levels are taken into account in the game. This application provides a novel approach to related literature for determining important marketing activities for online stores. Also, results will be important for Turkish practitioners since there are limited studies on determining important store attributes for Turkish customers.