Complex Dynamics of Mixed Triopoly Game with Quantity and Price Competition | Zendy

Jing Wang | Zendy; Zhenhua Bao | Zendy; Junqing Huang | Zendy; Yu-Jing Song | Zendy

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Complex Dynamics of Mixed Triopoly Game with Quantity and Price Competition

Author(s) -

Jing Wang,

Zhenhua Bao,

Junqing Huang,

Yu-Jing Song

Publication year - 2021

Publication title -

discrete dynamics in nature and society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.264

H-Index - 39

eISSN - 1607-887X

pISSN - 1026-0226

DOI - 10.1155/2021/9532340

Subject(s) - nash equilibrium , equilibrium point , mathematical economics , competition (biology) , chaotic , stability (learning theory) , boundary (topology) , economics , bifurcation , lyapunov exponent , mathematics , computer science , nonlinear system , physics , mathematical analysis , ecology , management , quantum mechanics , machine learning , biology , differential equation

This article investigates the dynamics of a mixed triopoly game in which a state-owned public firm competes against two private firms. In this game, the public firm and private firms are considered to be boundedly rational and naive, respectively. Based on both quantity and price competition, the game’s equilibrium points are calculated, and then the local stability of boundary points and the Nash equilibrium points is analyzed. Numerical simulations are presented to display the dynamic behaviors including bifurcation diagrams, maximal Lyapunov exponent, and sensitive dependence on initial conditions. The chaotic behavior of the two models has been stabilized on the Nash equilibrium point by using the delay feedback control method. The thresholds under price and quantity competition are also compared.

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