Research on the triopoly dynamic game model based on different rationalities and its chaos control

Based on the earlier research results, and combined with the actual competition in Chinese insurance market, the triopoly dynamic game model is built under the hypothesis that the oligarchs make adaptive decision, delayed bounded rational decision and bounded rational decision respectively. The existence of only Nash equilibrium in the system is analyzed theoretically, and its stability and the existence of Hopf bifurcation are also studied. The further numerical simulation result verified the accuracy of theoretical study and displayed more intuitively the dynamic behaviour of the system. From this we can conclude that in the process of considering delayed price game, the insurance company must control the value of delay parameter well and decrease his price adjustment speed properly. Only in this way they can make the system stable to its equilibrium state more rapidly. At last, the variable feedback control method is used to make control to the system, it makes the unstable system to the Nash equilibrium state again. Key–Words: Insurance market, Oligopoly, Dynamic game, Self-adaptive, Delay, Bounded rationality