| Game theory is a science of decision analysis in the case of the conflicts of interest. The typical problem studied is how some game players make their decision to meet their own interests when they conflict their interests with others in the same environment. In the course of playing games, the payoffs of both of the game players are basically judged by themselves in advance. However, they cannot make their precise judgment to their game results in advance, because of their limited cognition level, incompleteness of information, random fluctuation of systems. Therefore, it is a hot topic on how to play games in the case of uncertainties. Interval number plays an important and unique role in solving this problem. In this thesis, the problem of game theory is investigated with payoffs denoted by interval numbers, the main research contents are as follows:1. Since the key of solving the game theory problem with interval number payoffs is selection of interval number order relations. If order relations selected are different, the equilibriums obtained are not the same. Accordingly, the principle and method of the intervalnumber order relation selection are proposed and the features of different order relations are compared.2. Under some selected order relation, particular solutions and general solutions to Nash equilibrium of two-person complete information static game are defined and discussed, and the solving methods are also presented. Subsequently, an example is given to demonstrate how the methods is applied to practical problems and explain the phenomenon of the strategic selection in our practical life.3. The method of solving the problem of two-person complete information static game with interval number payoffs is generalized to the ones of n -person non-cooperative game and cooperative game with interval number payoffs. The existence of their equilibrium solutions is discussed and the methods of solving their particular solutions are also given.
|
PDF Full Text Request