Research on the price game model for four oligarchs with different decision rules and its chaos control

Based on the actual competition in the Chinese property insurance market, the repeated price game model for four oligarchs with different decision rules is built. On the basis of analyzing the stabilities of eight fixed points about the four-dimensional dynamic system, the Nash equilibrium and its local stable region are discussed mainly. Then the complexity of the four-dimensional discrete dynamic system and its evolutionary process are studied. Finally, the delay feedback control method is used to control the chaos. Numerical simulation results have shown that the influence which the change of price adjustment speed has on the movement of dynamic system has a sensitive dependence on the initial conditions, and there is a strong connection between the profit of each oligarch and the price adjustment speed or the control parameters, and the corresponding economic explanation to those phenomena will have important reference values to the realistic problems.

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