Solving game with interval-valued utilities

In interactive situations, it is very difficult to obtain exact utility of decision maker because decision makers interact and may also affect one another´s decision outcomes. The utilities of decision makers are represented by interval values which can expand the scope of application of the game theory. Solving the exact solution of the Nash equilibrium is very difficult, and so in this paper continuous mixed strategy space is replaced by discrete mixed strategy space in order to reduce the amount of computation. So finding the approximate solution (ε - Nash equilibrium) can be regarded as searching the optimal solution in a discrete space with genetic algorithm. Considering the characteristics of interval-valued utilities, deviation degree of interval-valued utilities is defined. Experimental studies have been performed for validation.