Complex dynamics and control of a dynamic R&amp;D Bertrand triopoly game model with bounded rational rule

In this paper, a dynamic two-stage Cournot duopoly game with R&D efforts is built. Then, the local stability of the equilibrium points are discussed, and the stability condition of the Nash equilibrium point is also deduced through Jury criterion. The complex dynamical behaviors of the built model are investigated by numerical simulations. We found that the unique route to chaos is flip bifurcation, and the increase of adjusting speed will cause the system to lose stability and produce more complex dynamic behavior. In addition, we also found the phenomenon of multistability in the given model. Several kinds of coexistence of attractors are shown. In particular, we found that boundary attractors can coexist with internal attractors, which also aggravates the complexity of the system. At last, the chaotic state in the built system has been successfully controlled.

Section: E Control Of Chaosmentioning

confidence: 99%

Section: E Control Of Chaosmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

Zhou

Chu

et al. 2020

“…Xin and Chen [35] investigate a master-slave Bertrand game model, which was proposed for upstream and downstream monopolies owned by different parties with bounded rationality. Tu and Wang [36] explore the complex dynamics of an R&D two-stage input competition triopoly game model with bounded rational expectations. Elsadany [37] analyzes the complex dynamics on a triopoly game with bounded rationality and radical form inverse demand function.…”

Section: Literature Reviewmentioning

confidence: 99%

Bertrand Game with Nash Bargaining Fairness Concern

Tan

2019

The classical Bertrand game is assumed that players are perfectly rational. However, many empirical researches indicate that people have bounded rational behavior with fairness concern, which is important in the two-person game and has attracted much attention. In this paper, fairness concern is incorporated into the Bertrand game with two homogeneous products and the effect of fairness concern on this extended Bertrand game is explored. Nash bargaining solution of player is applied to be his own fairness reference point. Then, a Bertrand game model with fairness concern is established, and its equilibrium price is also derived and analyzed. It is shown from some numerical examples that fairness concern and bargaining power of players have a significant influence on their equilibrium price, expected profits, and utilities. As a player gets more fair-minded, if the other player has a less focus on fairness, the price competition between them will be intensified and both of them suffer loss. Thus, fairness concern may be advantageous or disadvantageous for players. In most situations, the fairness concern behavior is not beneficial for players. Additionally, the effect of bargaining power is relative to fairness concern. A player who manufactures a low-cost product should have a weak bargaining power if he terribly focuses on fairness and should have a strong bargaining power if he pays little attention to fairness. However, a player who manufactures a high-cost product should have a weak bargaining power if he is rarely concerned about fairness. Anyway, the same bargaining power is the best for two players.

“…Researchers have adopted a variety of adjustment mechanisms, including horizontal product differentiation [31], a gradient adjustment mechanism [32], among others. Tu and Wang [33] proposed a dynamic competition triopoly game considering two-stage R&D input.…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis of Prefabrication Contractors’ Dynamic Price Competition in Mega Projects with Different Competition Strategies

Zhu

Shi

et al. 2018

This paper considers a repeated duopoly game of prefabrication contractors in mega infrastructure projects and assumes the contractors exhibit bounded rationality. Based on the theory of bifurcation of dynamical systems, a dynamic price competition model is constructed considering different competition strategies. Accordingly, the stability of the equilibrium point of the system is discussed considering different initial market capacities, and numerical simulation is performed. The results show the system has a unique equilibrium solution when initial capacity is high and the parameters meet certain conditions. The contractors’ price adjustment strategy has an important influence on system stability. However, an overly aggressive competition strategy is not conducive to system stability. Moreover, the system is sensitive to initial parameter values.