The Cournot–Bertrand model and the degree of product differentiation

Tremblay, Carol Horton; Tremblay, Victor J.

doi:10.1016/j.econlet.2011.02.011

Cited by 121 publications

(88 citation statements)

References 9 publications

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“…6 For a discussion of this bargaining approach, see Roth [15], McDonald and Solow [16], and Binmore, et al [17]. 7 For example, Binmore, et al [17] show that a player's bargaining power diminishes as the player becomes more impatient during the bargaining process or believes that there is a higher probability that negotiations will break down.…”

Section: Cournot Competitionmentioning

confidence: 99%

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Union Bargaining in an Oligopoly Market with Cournot-Bertrand Competition: Welfare and Policy Implications

Schroeder

Tremblay

2014

Economies

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Abstract:We investigate the welfare effect of union activity in a relatively new oligopoly model, the Cournot-Bertrand model, where one firm competes in output (a la Cournot) and the other firm competes in price (a la Bertrand). The Nash equilibrium prices, outputs, and profits are quite diverse in this model, with the competitive advantage going to the Cournot-type competitor. A comparison of the results from the Cournot-Bertrand model with those found in the traditional Cournot and Bertrand models reveals that firms and the union have a different preference ordering over labor market bargaining. These differences help explain why the empirical evidence does not support any one model of union bargaining. We also examine the welfare and policy implications of union activity in a Cournot-Bertrand setting.

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Section: Cournot Competitionmentioning

confidence: 99%

“…7 When a = 1, the union has all the power; when a = 0, all of the bargaining power goes to the firms. The Stage I game is solved by maximizing (5) with respect to w, given the best-reply functions in Equation (3).…”

Section: Cournot Competitionmentioning

confidence: 99%

Union Bargaining in an Oligopoly Market with Cournot-Bertrand Competition: Welfare and Policy Implications

Schroeder

Tremblay

2014

Economies

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“…Furthermore, Tremblay et al [21] have demonstrated that empirical evidence has led to the fact that this kind of competition is abundant. Recently, C. H. Tremblay and V. J. Tremblay [22] have shown the static properties of the Nash equilibrium of a Cournot-Bertrand duopoly according to product differentiation. Naimzada and Tramontana [23] have studied the dynamic properties of a Cournot duopoly game with product differentiation using linearity of demand and cost objective functions.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Askar

Al-khedhairi

2017

Discrete Dynamics in Nature and Society

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Many researchers have used quadratic utility function to study its influences on economic games with product differentiation. Such games include Cournot, Bertrand, and a mixed-type game called Cournot-Bertrand. Within this paper, a cubic utility function that is derived from a constant elasticity of substitution production function (CES) is introduced. This cubic function is more desirable than the quadratic one besides its amenability to efficiency analysis. Based on that utility a two-dimensional Cournot duopoly game with horizontal product differentiation is modeled using a discrete time scale. Two different types of games are studied in this paper. In the first game, firms are updating their output production using the traditional bounded rationality approach. In the second game, firms adopt Puu's mechanism to update their productions. Puu's mechanism does not require any information about the profit function; instead it needs both firms to know their production and their profits in the past time periods. In both scenarios, an explicit form for the Nash equilibrium point is obtained under certain conditions. The stability analysis of Nash point is considered. Furthermore, some numerical simulations are carried out to confirm the chaotic behavior of Nash equilibrium point. This analysis includes bifurcation, attractor, maximum Lyapunov exponent, and sensitivity to initial conditions.

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“…H. Tremblay and V. J. Tremblay [5] introduced a Cournot-Bertrand duopoly model in a Cournot-type firm and a Bertrand-type firm based on the degree of product differentiation. The Cournot-Bertrand equilibrium was calculated and the analysis of the equilibrium was also conducted.…”

Section: Introductionmentioning

confidence: 99%

Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

Ma¹,

Di²,

Ren³

2017

Complexity

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Apart from the price fluctuation, the retailers' service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer's service level which influences the market demand decided by customers' preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

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The Cournot–Bertrand model and the degree of product differentiation

Cited by 121 publications

References 9 publications

Union Bargaining in an Oligopoly Market with Cournot-Bertrand Competition: Welfare and Policy Implications

Union Bargaining in an Oligopoly Market with Cournot-Bertrand Competition: Welfare and Policy Implications

Analysis of Nonlinear Duopoly Games with Product Differentiation: Stability, Global Dynamics, and Control

Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

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