Multiplayer Fuzzy Game Models and An Application

Abstract

Considering markets of today’s competitive environment and conditions where strategic goals of countries conflict, new situations stand out. These situations were not common in the beginning of the 20th century and now the effects of them gradually increase.

First of all, in the competitive environment of modern times, any goal has more than two aspiring sides. This situation has revealed the necessity of the parties to review many options to achieve the goal, to analyze opportunities multiple coalitions and the individual benefit to be obtained in different strategies. Additionally, uncertainties are quite high in the competitive environment of modern times. Global competition has caused uncertainties and differences in various definitions. Thus, fuzzy definitions gain importance day by day.

Finally, variable risk levels require parties in competitive environment to dynamically examine their benefits continuously.

Considering all the situations mentioned above, competition and conflict environments contain multilateral, fuzzified and variable risks. In recent studies, multiplayer game models and fuzzy game models are frequently examined by academicians aiming to model today's conflict environments. Multiplayer fuzzy game models are relatively less discussed and different solution approaches are used. In the first approach, Tsurumi examines the players' participation in possible coalitions at different rates and a solution approach is presented with the help of Choquet integral. Mares, on the other hand, suggested an approach in which the parties have fuzzy payoffs. For this purpose, Shapley Vector was processed in a fuzzy way and the contribution of the parties to the game was calculated with the help of the fuzzy Shapley value by Mares. The purpose of this thesis is to calculate the fuzzy Shapley value with the method of Mares, to determine the critical α value that players will enter to coalition with the individual rationality rule which is offered in the solution of cooperative games, and to examine players’ reaction in different uncertainty environment. With this method, that has not been studied before in the literature, it is evaluated that the players can decide whether to participate in coalition or not in cases of changing uncertainty.

The effectiveness of the proposed method has been demonstrated by applying it on real life model. For this purpose a simulation is prepared. In the problem, a conflict environment is modeled so as to obtain the right to use underground resources where four countries are parties. The categories were determined by taking the expert opinions to be used in determining the effectiveness and strengths of the countries. The strengths of the countries have been calculated by using these categories again with experts. The value of all possible coalitions that the countries will establish with each other is calculated with the help of expert opinion on the basis of same categories. Then, the obtained data were fuzzified and fuzzy Shapley values were calculated. Each country's individual contribution to the game and their own strengths were compared at different risk levels with the help of α-values and the most reasonable risk level is calculated in terms of individual rationality. With this method, it has been investigated that what risk levels would be meaningful for countries to enter the conflict environment that includes possible coalitions.