Saddle point equilibrium model for uncertain discrete systems

Uncertainty theory is a newly founded mathematical tool for modeling subjective indeterminacy. This type of indeterminate events is described as uncertain events and measured by belief degrees. In this paper, a saddle point equilibrium game model is studied for an uncertain discrete system, where the system is disturbed by an uncertain event at each stage. Applying Bellman’s dynamic programming approach, recurrence equations for this model are presented. The explicit solution of a bang–bang game model for the uncertain discrete system is obtained. Furthermore, for general cases, a hybrid intelligent algorithm is provided to approximate the solution numerically. Finally, a discrete game of duopoly is discussed to show the effectiveness of our results.