Theocharis Problem Reconsidered in Differentiated Oligopoly

Matsumoto, Akio; Szidarovszky, Ferenc

doi:10.1155/2014/630351

Cited by 3 publications

(6 citation statements)

References 19 publications

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“…In Figure 6(B), we see that the bifurcation diagram gets more complicated and various dynamics can emerge. Lastly, we simulate system (11) with n = 9: The shape of the stability switching curve is di¤erent from those with smaller n. In Figure 7(A), the positivesloping dotted line is the diagonal, the dotted-red line is L 2 (0; 0) as before and 18 Lastly, we simulate system (11) with n = 9. The shape of the stability switching curve is different from those with smaller n. In Figure 7A, the positive-sloping dotted line is the diagonal, the dotted-red line is L − 2 (0, 0) as before and the black dots are the starting or ending points of the segments.…”

Section: Lemma 3 In the Case Of Nmentioning

confidence: 97%

“…System (11) has the same stationary point as system (1). The homogeneous part of its linearized version isẋ…”

Section: Growth Rate Dynamicsmentioning

confidence: 99%

“…By Lemma 4, both line segments head to point a; the terminal point as ! increases to 2K: We simulate the model (11) along the diagonal (i.e., 1 = 2 ) and the dotted horizontal line at 2 = 3 (i,e., 1 6 = 2 ) in Figure 5(A). Since we …nd qualitatively no big di¤erences between these simulation results as in Figures 4(A) and 4(B), we depict only the bifurcation diagram with di¤erent delays in Figure 5(B).…”

Section: Lemma 3 In the Case Of Nmentioning

confidence: 99%

“…Dynamic system (11) examines the birth of complicated dynamics through a period-doubling bifurcation and the occurrence of stability loss and gain. Needless to say, time delays play prominent roles.…”

Section: Stability Indexmentioning

confidence: 99%

“…The early results up to the mid-70s are summarized in Okuguchi [4] and their multiproduct generalizations are presented in Okuguchi and Szidarovszky [5]. Different aspects of the classical Theocharis model were then examined by several authors including Canovas et al [6], Hommes et al [7], Lampart [8], Puu [9,10], Matsumoto and Szidarovszky [11] among others. Nonlinear models are discussed in Bischi et al [12] and their extensions including delays are examined in Matsumoto and Szidarovszky [13].…”

Section: Introductionmentioning

confidence: 99%

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Delay Stability of n-Firm Cournot Oligopolies

Matsumoto

Szidarovszky

2020

Mathematics

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The dynamic behavior of n-firm oligopolies is examined without product differentiation and with linear price and cost functions. Continuous time scales are assumed with best response dynamics, in which case the equilibrium is asymptotically stable without delays. The firms are assumed to face both implementation and information delays. If the delays are equal, then the model is a single delay case, and the equilibrium is oscillatory stable if the delay is small, at the threshold stability is lost by Hopf bifurcation with cyclic behavior, and for larger delays, the trajectories show expanding cycles. In the case of the non-equal delays, the stability switching curves are constructed and the directions of stability switches are determined. In the case of growth rate dynamics, the local behavior of the trajectories is similar to that of the best response dynamics. Simulation studies verify and illustrate the theoretical findings.

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Section: Lemma 3 In the Case Of Nmentioning

confidence: 97%

“…System (11) has the same stationary point as system (1). The homogeneous part of its linearized version isẋ…”

Section: Growth Rate Dynamicsmentioning

confidence: 99%

Section: Lemma 3 In the Case Of Nmentioning

confidence: 99%

Section: Stability Indexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Delay Stability of n-Firm Cournot Oligopolies

Matsumoto

Szidarovszky

2020

Mathematics

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Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production

Grisáková

Štetka

2022

Games

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The subject of this study is an oligopolistic market in which three firms operate in an environment of quantitative competition known as the Cournot oligopoly model. Firms and their production are differentiated, which brings the theoretical model closer to real market conditions. The main objective was to expand the Cournot duopoly and add another firm, resulting in an oligopolistic market structure assuming a partially differentiated production and coalition strategy between two firms. This article contains an oligopolistic model specifically designed for three different types of expectations, and has been applied to find and verify the stability of the net equilibrium of oligopolists. The market of telecommunication operators in Slovakia was selected as a real market case with accessible data on an oligopoly with three companies and partial differentiation. There are studies in which the authors limit their considerations to a certain number of repetitions of oligopolistic games. An infinite time interval is considered here. Three types of future expectations were considered: a simple dynamic model (or naïve expectations) in which the oligopolist assumes that its competitors will behave in the future based on their response functions, an adaptive expectations model in which the oligopolist considers a weighted average of the quantities offered by its competitors, and real expectations in which firms behave as rational players and do not have complete information about demand and offer output based on expected marginal profit. While the presented model proved to be stable under naïve and adaptive expectations, no stable equilibrium was found under real expectations and further results indicate a chaotic behavior.

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Monopoly conditions in a Cournot-Theocharis oligopoly model under adaptive expectations

Cánovas¹,

Muñoz-Guillermo²

2022

DCDS-B

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We consider the Cournot-Theocharis oligopoly model, where firms make their choices under adaptive expectations. Following [2], we assume that quantities cannot be negative, which implies that the model is nonlinear. The stability of the equilibrium point in the general case is analyzed. We focus on the conditions for which the number of competitors is reduced to a monopoly. In particular, we find necessary and sufficient conditions giving an analytic proof of the convergence to oligopoly to monopoly.

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Theocharis Problem Reconsidered in Differentiated Oligopoly

Cited by 3 publications

References 19 publications

Delay Stability of n-Firm Cournot Oligopolies

Delay Stability of n-Firm Cournot Oligopolies

Cournot’s Oligopoly Equilibrium under Different Expectations and Differentiated Production

Monopoly conditions in a Cournot-Theocharis oligopoly model under adaptive expectations

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