Bifurcation Analysis and Tax/subsidy Approach in Noncooperative Dynamical Systems

A new type of bifurcations is illustrated for Nash equilibrium in the noncooperative systems with a squarely bounded state space. In this type of bifurcations, a new Nash equilibrium appears with two new branches, where one of them disappears with the initial branch and the other one holds the same profile as the bifurcation parameter increases. The Nash equilibrium inside the state space is founded as a unstable Nash equilibrium in the noncooperative dynamical system. To improve the efficiency of the system, we propose a zero-sum tax/subsidy approach to stabilize the unstable Nash equilibrium without using the information of agents' personal sensitivity parameter.