A Cournot duopoly game with heterogeneous players: Nonlinear dynamics of the gradient rule versus local monopolistic approach

Cavalli, Fausto; Naimzada, Ahmad

doi:10.1016/j.amc.2014.10.031

Cited by 33 publications

(39 citation statements)

References 24 publications

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“…In particular, it is shown that, when the cost ratio is sufficiently favorable to the firm which adopts the gradient-like decisional mechanism, the scenario presents a Neimark-Sacker bifurcation, while the flip bifurcation occurs when the costs structure is favorable to the firm using linear approximation. This result improves the knowledges about dynamics involving gradient rule, and further confirms recent studies showing that both Neimark-Sacker and flip bifurcations appear to be the possible destabilization, as shown in [15,16,12,18,13]), especially when a gradient-rule dynamic is present.…”

Section: Introductionsupporting

confidence: 89%

“…In this work, we consider two different mechanisms which imply a reduced degree of rationality, the "Local Monopolistic Approximation" (LMA) and the gradient adjustment mechanism. The description of these two mechanism can be found in [13]. For the sake of completeness, we briefly summarize them.…”

Section: Modelmentioning

confidence: 99%

“…In particular, it can be constant with respect to the produced quantity or endogenously dependent from it, to enforce its dependence on the firm size. The constant reactivity gradient mechanism is discussed in the book of Varian [10] and by Corchon and Mas-Colell in [11], while duopolies involving a firm following it were studied by Angelini et al [12] and Cavalli et al [13]. Conversely, the endogenous reaction was studied by Bischi and Naimzada [14], Bischi et al [15,16], Agiza et al [17], Tramontana [18] and more recently by Askar in [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

Cavalli

Naimzada

Tramontana

2015

Communications in Nonlinear Science and Numerical Simulation

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We study a heterogeneous duopolistic Cournotian game, in which the firms, producing a homogeneous good, have reduced rationality and respectively adopt a "Local Monopolistic Approximation" (LMA) and a gradient-based approach with endogenous reactivity, in an economy characterized by isoelastic demand function and linear total costs. We give conditions on reactivity and marginal costs under which the solution converges to the Cournot-Nash equilibrium. Moreover, we compare the stability regions of the proposed oligopoly to a similar one, in which the LMA firm is replaced by a best response firm, which is more rational than the LMA firm. We show that, depending on costs ratio, the equilibrium can lose its stability in two different ways, through both a flip and a Neimark-Sacker bifurcation. We show that the nonlinear, noninvertible map describing the model can give rise to several coexisting stable attractors (multistability). We analytically investigate the shape of the basins of attractions, in particular proving the existence of regions known in the literature as lobes.

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Section: Introductionsupporting

confidence: 89%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

Cavalli

Naimzada

Tramontana

2015

Communications in Nonlinear Science and Numerical Simulation

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“…Conversely, the works concerning heterogeneous oligopolies, in which at least two firms adopt different decision mechanisms, mainly focused on studying different coupling of distinct decision mechanisms in oligopolies of fixed reduced sizes, usually duopolies or triopolies. We mention the papers by Agiza et al [8][9][10][11][12], Angelini et al [13], Bischi et al [14][15][16], Matsumoto [17], Cavalli et al [18][19][20] and Tramontana [21].…”

Section: Introductionmentioning

confidence: 98%

Heterogeneity and the (de)stabilizing role of rationality

Cavalli

Naimzada

Pireddu

2015

Chaos, Solitons & Fractals

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a r t i c l e i n f o Article history: Available online xxx a b s t r a c tIn this paper we study oligopolies of generic size consisting of heterogeneous firms, which adopt best response adjustment mechanisms with either perfect foresight (rational firms) or static expectations (naive firms). Assuming an isoelastic demand function and possibly different marginal costs for the two groups of firms, we focus on the local stability of the Nash equilibrium. We show that, with respect to the oligopoly composition, described in terms of the fraction of rational firms, different scenarios are possible. We find that a high rationality degree may not always guarantee stability, in particular when rational firms have sufficiently larger marginal costs. In fact, in this situation, increasing the fraction of rational firms can even introduce instability. Besides the usual scenarios in which replacing some naive firms with rational ones leads to a stabilization of (or at least keeps unchanged) the dynamics, we provide a family of situations, characterized by costs ratio favorable to naive firms, in which equilibrium loses its stability when naive firms are replaced by rational ones. The results we present are both analytical and simulative.

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“…Following these studies, the model was extended to the case of nonlinear demand function [6,7,8]. Another extension is the Cournot duopoly game with heterogeneous players, where the two players adopt different decision-making strategies [9,10,11,12,13,14]. In addition, the dynamic Cournot duopoly game with time delay [15] as well as the Cournot triopoly with bounded rationality [16,17] has been studied.…”

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confidence: 99%

Effect of information asymmetry in Cournot duopoly game with bounded rationality

Ueda

2019

Applied Mathematics and Computation

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We investigate the effect of information asymmetry on a dynamic Cournot duopoly game with bounded rationality. Concretely, we study how one player's possession of information about the other player's behavior in a duopoly affects the stability of the Cournot-Nash equilibrium. We theoretically and numerically show that the information stabilizes the Cournot-Nash equilibrium and suppresses chaotic behavior in the duopoly.

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A Cournot duopoly game with heterogeneous players: Nonlinear dynamics of the gradient rule versus local monopolistic approach

Cited by 33 publications

References 24 publications

Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

Nonlinear dynamics and global analysis of a heterogeneous Cournot duopoly with a local monopolistic approach versus a gradient rule with endogenous reactivity

Heterogeneity and the (de)stabilizing role of rationality

Effect of information asymmetry in Cournot duopoly game with bounded rationality

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