New results on stable region of Nash equilibrium of output game model
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We obtains that the real stable region of Nash equilibrium of output game model is smaller than that in general. Because of the prisoners' dilemma, players would not select some of the values of parameters, though those points of parameters' orbit will tend to the Nash equilibrium point. That is, players' strategies are unstable in those values. In order to discuss this problem, we introduce a duopoly output dynamical model. We use numerical simulation to analyze the initial output and the decisive parameters' influences on the speed of the system's evolution convergence to Nash equilibrium, and we measure performances of the model in various period states and chaotic state by using the index of average profits. It is found that the optimal strategy locates in the stable region of Nash equilibrium, and aggregate profits are not sensitive to initial output in certain neighborhood of Nash equilibrium and the decisive parameters in their majority of stable region of Nash equilibrium neither. Impact of the decisive parameters on the speed of the initial output convergent to Nash equilibrium and the prisoners' dilemma in game theory are the main reason yielding uneven parts in both sides of 3-dimensions simulation figure. The projection of the even parts of the 3-dimensions simulation on the plane of parameters is the real stable region of the Nash equilibrium point. It is necessary to ascertain the stable region of Nash equilibrium point by combining the Jury' condition with some performance indices in economic systems, such as average profit, aggregate profits, aggregate sales revenues and so on. We may determine the factual stable region by using the indifference character of utilities of players in the traditional stable region given by Jury's condition. We also obtain that players should pay attention to the performance of economic entity in various period states. 2007 Elsevier Inc. All rights reserved.