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Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

Feng Liu

http://orcid.org/0000-0002-3528-3472

School of Economics, Hefei University of Technology, Fei Cui Road 420, Hefei, P. R. China

Research Center of Industry Information, Hefei University of Technology, Fei Cui Road 420, Hefei, P. R. China

E-mail Address: dwoffice@126.com

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and

Yaguang Li

School of Economics, Hefei University of Technology, Fei Cui Road 420, Hefei, P. R. China

Research Center of Industry Information, Hefei University of Technology, Fei Cui Road 420, Hefei, P. R. China

E-mail Address: yaguangli926@163.com

Corresponding author

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https://doi.org/10.1142/S0218127416501832Cited by:3 (Source: Crossref)

Abstract

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

Keywords:

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