Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production

Zhang, Yahui; Zhou, Wei; Chu, Tong; Chu, Yan-Dong; Jiang, Yu

doi:10.1007/s11071-017-3912-4

Cited by 43 publications

(25 citation statements)

References 33 publications

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“…However, models à la Cournot have also been used in evolutionary settings to study, for example, reinforcement learning effects [30], implications of social and individual learning [31], impact of competing behavioral rules [32], effects of firm entry and exit on industry dynamics [33,34], and the influence of product differentiation on equilibrium stability [35]. Much recent work takes Cournot competition in dynamic settings as the steppingstone to study nonlinear behavior and equilibrium stability (e.g., [36,37,38,39]).…”

Section: Firm Competition In Evolving Attribute Spacesmentioning

confidence: 99%

The coevolution of the firm and the product attribute space

2020

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Traditionally, firm competition has been studied in contexts where the dimensionality of the product attribute space is given, and firms deploy their strategies constrained by this space. However, firms may exert influence on the local structure of the product attribute space by offering product variants with new attributes. As a result, the geometry of the product attribute space would change endogenously through firms' actions, and this emergent new geometry modifies the conditions for subsequent firm behavior. By focusing on this interplay between actors and conditions, we explore the co-evolution of the firm and the product attribute space. Through a multi-variant Cournot competition framework, we develop a computational model in which firms invest to differentiate their products from other variants, but as minimally as possible so that demand from closely similar existing variants can be stolen. We introduce the fraction dimensionality of the attribute space as our critical independent variable, to reflect saturation of the space with product varieties. The simulation reveals that while new product variants are typically introduced by firms with scale economies, their performance gap with firms without scale economies reduces as fraction dimensionality increases. This indicates that space geometry evolution may favor small-scale players, even when their large-scale competitors are the driving force behind attribute space changes. 1 Introduction: Commodity space evolution Attribute spaces display how demand for, and supply of, organizational services distributes over a number of attributes, or dimensions, that characterize the offerings [1]. As the number of product attributes taken into account by economic actors is a natural number, we straightforwardly associate the complexity of the attribute space with its positive integer dimensionality. The attribute space can be a commodity space spun by product characteristics that prospective customers evaluate [1, 2, 3], a market place that combines product design and product quality features [4], or a political issue space within which political representation is offered [5, 6]. In organization science, this can be a Blau-space [7] dimensioned by people's

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Section: Firm Competition In Evolving Attribute Spacesmentioning

confidence: 99%

The coevolution of the firm and the product attribute space

2020

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“…Bischi et al [14] analyzed the global bifurcation of a nonlinear duopoly model with adaptive expectations using the critical curve, and the equilibrium selection problem arising in this model was also discussed by them. Zhou et al [15] and Zhang et al [16] studied the complex dynamical behaviors of the twostage Cournot duopoly model with R&D spillover effect.…”

Section: Introductionmentioning

confidence: 99%

Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product

et al. 2020

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In this paper, a mixed duopoly dynamic model with bounded rationality is built, where a public-private joint venture and a private enterprise produce homogeneous products and compete in the same market. The purpose of this research is to study the stability and the multistability of the established model. The local stability of all the equilibrium points is discussed by using Jury condition, and the stability region of the Nash equilibrium point has been given. A special fractal structure called “hub of periodicity” has been found in the two-parameter space by numerical simulation. In addition, the phenomena of multistability (also called coexistence of multiple attractors) are also studied using basins of attraction and 1-D bifurcation diagrams with adiabatic initial conditions. We find that there are two different coexistences of multiple attractors. And, the fractal structure of the attracting basin is also analyzed, and the formation mechanisms of “holes” and “contact” bifurcation have been revealed. At last, the long-term profits of the enterprises are studied. We find that some enterprises can even make more profits under a chaotic circumstance.

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“…And hence, the economists and the mathematicians can simulate the complex dynamical behavior of oligopoly market by using computer technology. Recently, a large number of scholars have improved the oligopoly models, and introduced bounded rationality (see [2,3]), incomplete information [4], time delay [5], market entering and entering barriers [6], differentiated products [7] and other factors [8,9] into the classical oligopoly models, and the bifurcation and chaos phenomenon were founded in the process of repeated game.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamical Behavior of a Bounded Rational Duopoly Game with Consumer Surplus

Zhou¹,

Chu²

2020

Research Advances in Chaos Theory

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In this chapter, we assume that two bounded rational firms not only pursue profit maximization but also take consumer surplus into account, so the objections of all the firms are combination of their profits and the consumer surplus. And then a dynamical duopoly Cournot model with bounded rationality is established. The existence and stability of the boundary equilibrium points and the Nash equilibrium of the model are discussed, respectively. And then the stability condition of the Nash equilibrium is given. The complex dynamical behavior of the system varies with parameters in the parameter space is studied by using the so-called 2D bifurcation diagram. The coexistence of multiple attractors is discussed through analyzing basins of attraction. It is found that not only two attractors can coexist, but also three or even four attractors may coexist in the established model. Then, the topological structure of basins of attraction and the global dynamics of the system are discussed through invertible map, critical curve and transverse Lyapunov exponent. At last, the synchronization phenomenon of the built model is studied.

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Complex dynamics analysis for a two-stage Cournot duopoly game of semi-collusion in production

Cited by 43 publications

References 33 publications

The coevolution of the firm and the product attribute space

The coevolution of the firm and the product attribute space

Stability and Multistability of a Bounded Rational Mixed Duopoly Model with Homogeneous Product

Complex Dynamical Behavior of a Bounded Rational Duopoly Game with Consumer Surplus

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