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Research on the price game and the application of delayed decision in oligopoly insurance market

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Abstract

In the oligopoly insurance market, we assumed that some oligarchs make two-period delay decisions in bounded rationality and expectation, respectively, and others make decisions with bounded rationality without the condition of delay. There also exist two cases in which only one oligarch makes a delayed decision and two oligarchs make delayed decisions at the same time. Based on the analysis of these situations, we established the corresponding dynamic price game models. We then performed a numerical simulation to the complexity state of the system with different conditions such as stability, bifurcation, and chaos, and analyzed the profits of different oligarchs when the system is in different states. The results showed that when only one oligarch makes a delayed decision, with the decrease in the price weight of period t and increase in that of periods t−1 and t−2, the system’s stable region in the direction of the price adjustment of the oligarch with a delayed decision gets smaller. However, when there are two oligarchs with a delayed decision in the system, in the case where the delay parameters of oligarch 1 remain unchanged and the price parameters of different periods of oligarch 2 change, the system’s stable region in the direction of the price adjustment of oligarch 1 does not have the obvious change as that when only one oligarch makes a delayed decision. This showed that the sensibility of one oligarch in the direction of its own price adjustment is lower than other oligarchs. In addition, in the same system with delay and when the system is in chaos, the total profit of the oligarchs is obviously less than that when the system is in a stable state. However, the use of a delayed decision may not enhance the oligarch’s competitive advantages. Finally, the variable feedback control method is used to effectively control the chaos in the system.

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Acknowledgements

This work was supported by Doctoral Fund of Ministry of Education of China 20090032110031 and National Natural Science Foundation of China 61273231.

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Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Ma Junhai & Zhang Junling

  2. School of Economics and Management, Tianjin Vocational Institute, Tianjin, 300410, China

    Zhang Junling

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  1. Ma Junhai
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  2. Zhang Junling
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Correspondence to Ma Junhai.

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Junhai, M., Junling, Z. Research on the price game and the application of delayed decision in oligopoly insurance market. Nonlinear Dyn 70, 2327–2341 (2012). https://doi.org/10.1007/s11071-012-0566-0

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  • DOI: https://doi.org/10.1007/s11071-012-0566-0

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