title: Price game and chaos control among three oligarchs with different rationalities in property insurance market.
abstract: Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.
authors.affiliation: College of Management and Economics, Tianjin University, Tianjin 300072, China.
authors.forename: Junhai
authors.initials: J
authors.lastname: Ma
authors.forename: Junling
authors.initials: J
authors.lastname: Zhang