Fuzzy Ultimatum Game Model

The Ultimatum Game is the main focus of this thesis. Firstly, it introduces the essential knowledge of Game Theory and basic models of the Ultimatum Game. The limitations of assumption of players and mathematical tools of study are analyzed. To overcome these limitations, this thesis combines the study of Behavioral Game Theory and Fuzzy Theory. Based on the theory of fuzzy variables, the Ultimatum Game has been modeled with fuzzy preferences from the aspects of Behavioral Game Theory. It tries to make a better explanation for the data and induce better prediction and guidance for the real human activities. By analyzing the numerical example using the model provided in this thesis, it shows that it can explain well the data in the Ultimatum Game experiments.This thesis is constructed as follows: firstly, problems arising in the development of Game Theory and the current study are introduced. Secondly, fundamental knowledge of standard Game Theory and predictions made by standard Game Theory are introduced. Without the evolutional parameters, three typical behavioral game models are introduced in which all parameters are crisp. Based on the above chapters, a fuzzy ultimatum game model is presented in which the players' altruism preferences are fuzzy variables. With a numerical example, the data is analyzed by this fuzzy model. Another model with evolutional parameters is introduced.