Computation of the stability and complexity about triopoly price game model with delay decision
type: Item
instance of: scholarly article
title: Computation of the stability and complexity about triopoly price game model with delay decision
zbMATH Open document ID: 1416.91273
DOI: 10.1155/2017/2717352
author: Yuling Wang
author: Shubing Guo
author: Shide Duan
published in: Advances in Mathematical Physics
publication date: 2018-10-23T00:00:00Z
review text: Summary: We develop the price game model based on the entropy theory and chaos theory, considering the three enterprises are bounded rationality and using the cost function under the resource constraints; that is, the yield increase will bring increased costs. The enterprises of new model adopt the delay decision with the delay parameters \(\tau_1\) and \(\tau_2\), respectively. According to the change of delay parameters \(\tau_1\) and \(\tau_2\), the bifurcation, stability, and chaos of the system are discussed, and the change of entropy when the system is far away from equilibrium is considered. Prices and profits are found to lose stability and the evolution of the system tends to the equilibrium state of maximum entropy. And it has a big fluctuation with the increase of \(\tau_1\) and \(\tau_2\). In the end, the chaos is controlled effectively. The entropy of the system decreases, and the interior reverts to order. The results of this study are of great significance for avoiding the chaos when the enterprises make price decisions.
Mathematics Subject Classification ID: 91B54
Mathematics Subject Classification ID: 91B24
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 91A40
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 6962602
zbMATH Keywords: stability
zbMATH Keywords: complexity
zbMATH Keywords: triopoly price game model
zbMATH Keywords: entropy theory
zbMATH Keywords: chaos theory
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/2717352
OpenAlex ID: W2605997950
Wikidata QID: Q59142341
cites work: The dynamics of a Bertrand duopoly with differentiated products: Synchronization, intermittency and global dynamics
cites work: Complex dynamics of duopoly game with heterogeneous players: a further analysis of the output model
cites work: Equilibrium stability of a nonlinear heterogeneous duopoly game with extrapolative foresight
cites work: Study on a 3-dimensional game model with delayed bounded rationality
cites work: Q4504056
cites work: Analysis of the stability and Hopf bifurcation of money supply delay in complex macroeconomic models
cites work: Complexity analysis of dynamic noncooperative game models for closed-loop supply chain with product recovery
cites work: Theory of functional differential equations. 2nd ed
cites work: Complexity analysis research of financial and economic system under the condition of three parameters' change circumstances
description: scientific article; zbMATH DE number 6962602