A Bertrand Duopoly Game with Long-Memory Effects

Xin, Baogui; Cao, Fuliang; Peng, Wei; Elsadany, A. A.

doi:10.1155/2020/2924169

Cited by 9 publications

(17 citation statements)

References 32 publications

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“…When the market structure is stable enough at time t, p i (t + 1) are approximately equal to p i (t). Setting p 1 (t + 1) � p 1 (t) and p 2 (t + 1) � p 2 (t) in equation (12), we can get the following equilibria:…”

Section: Equilibrium Points and Local Stabilitymentioning

confidence: 99%

“…E 1 represents that every IC has no price; E 2 and E 3 represent the monopolies IC 1 and IC 2 , respectively; and E 4 represents both ICs competing in a duopoly game with equilibrium prices of p * 1 and p * 2 . To analyze the local stability of the equilibrium points, we consider the Jacobian matrix of system (12), which can be given by…”

Section: Equilibrium Points and Local Stabilitymentioning

confidence: 99%

“…Askar and Alkhedhairi [6] introduced two different Bertrand duopoly models where the first one is the competition of price in which each player wants to maximize its relative profit, and the second model is the classic Bertrand competition in which the players want to maximize their profits. ere is still some literature which studies the Bertrand game theory and the complexity of the dynamical system; see [7][8][9][10][11][12]. e above price game models assume that firms play simultaneous-move games; however, the competition among oligarchs in the real market is mostly a dynamic game or sequential game.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

Wei

Wang

et al. 2021

Discrete Dynamics in Nature and Society

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This paper investigates the dynamical behaviors of a Stackelberg mixed duopoly game with price competition in the insurance market, involving one state-owned public insurance company and one private insurance company. We study and compare the stability conditions for the Nash equilibrium points of two sequential-move games, public leadership, and private leadership games. Numerical simulations present complicated dynamic behaviors. It is shown that the Nash equilibrium becomes unstable as the price adjustment speed increases, and the system eventually becomes chaotic via flip bifurcation. Moreover, the time-delayed feedback control is used to force the system back to stability.

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Section: Equilibrium Points and Local Stabilitymentioning

confidence: 99%

Section: Equilibrium Points and Local Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

Wei

Wang

et al. 2021

Discrete Dynamics in Nature and Society

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“…In traditional game theory, it is often assumed that participants are bounded rational and that participants are fully informed; however, the problem of incomplete information and bounded rationality is evident due to the complexity of the economic environment [19]. Evolutionary game is studied with a bounded rational group of participants [20][21][22][23][24][25][26].…”

Section: Evolutionary Game Modelmentioning

confidence: 99%

Complex Dynamic Analysis for Game Model under Different Regulatory Levels in China’s Housing Rental Market

Qin

Yuan

et al. 2020

Complexity

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In this paper, we construct an evolutionary game model of government and real estate operators (long-term apartment rental companies) in the housing rental market in the context of financial institutions and public participation in regulation and analyze the effects of different regulatory levels of financial institutions and the public on the evolutionary results through model solving and numerical simulation. The results show that, under five different levels of supervision, financial institutions and the public have different evolutionary and stable strategies; financial institutions’ participation in supervision can effectively reduce the cost of government supervision and promote the government’s evolution towards strict supervision. It is difficult for real estate operators to evolve naturally towards keeping their promises when the probability of the social public or financial institutions participating in regulation is low. Only when the probability of social public and financial institutions participating in regulation reaches a certain level will real estate operators be inclined to keep their promises.

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“…Few papers have considered the effect of delays on market share dynamics models with controls, even though there has been a considerable amount of research on Cournot and Bertrand duopoly models with delays [8]- [12]. Cournot type models generally consider the control variables to be the quantities of a product produced and sold and make assumptions on the inverse demand functions which determine price and, as a result, profit.…”

Section: Introductionmentioning

confidence: 99%

Implementation and Adoption Delays in Market Share Models Under Feedback Advertising Policies

Aliaga

Bhaya

2021

IEEE Access

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This paper proposes definitions of implementation and adoption delays, arising from firm and client behaviors, in the context of market share dynamics. Information delay refers to the existence of lags in the information used for the advertising policy, while adoption delay refers to the existence of a lag in the effect of the advertising policy. These are natural lags in the flow of information and have not been considered in several models proposed in the literature. In this paper, these delays are introduced into recently proposed extensions of the Vidale-Wolfe-Deal and Lanchester models of market share dynamics subjected to affine advertising control policies. Conditions for stability of the equilibrium market share are derived. In addition, it is shown that Hopf bifurcations leading to oscillatory behavior exist for certain parameter values, and corresponding conditions for these are given. The main results are: the equilibrium market shares of the extended Vidale-Wolfe-Deal and Lanchester models are both robust to implementation delays, but, in the case of adoption delays, for both models, numerical results show that there is a critical value such that if the sum of the adoption delays exceeds this value, there is an onset of oscillations of market shares, through a Hopf bifurcation.

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A Bertrand Duopoly Game with Long-Memory Effects

Cited by 9 publications

References 32 publications

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

Dynamics and Stability Analysis of a Stackelberg Mixed Duopoly Game with Price Competition in Insurance Market

Complex Dynamic Analysis for Game Model under Different Regulatory Levels in China’s Housing Rental Market

Implementation and Adoption Delays in Market Share Models Under Feedback Advertising Policies

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