Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&amp;D spillover and product differentiation

Zhou, Jie; Zhou, Wei; Chu, Tong; Chang, Yunlong; Huang, Meng-jia

doi:10.1016/j.amc.2018.09.004

Cited by 56 publications

(38 citation statements)

References 29 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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“…Wang et al [16] Product differentiation + endogenous product substitutability theory Zhou et al [17] Product differentiation + bifurcation, intermittent chaos, and multi-stability Askar and Al-Khedhairi [18] Product differentiation + nonlinear duopoly games T 2: e literature and summary information about product differentiation theory in industry application.…”

Section: Researchermentioning

confidence: 99%

Research on the Influence of Bounded Rationality and Product Differentiation on the Stability of Steel Industry Market

Duan

Zeng-lin

et al. 2020

Discrete Dynamics in Nature and Society

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At present, the problems of homogenization and low quality in China’s iron and steel industry are particularly prominent and the ability of the enterprises to cope with change is insufficient. Adopting product differentiation strategy and dynamic adjustment strategy can allow steel enterprises and the industry to better adapt to future changes. By introducing the product differentiation degree (substitution coefficient) and the bounded rationality strategy to simulate these two strategic means, this paper constructs an extended two-stage dynamic game model to analyse the dynamic game scenarios and steel market stability in China. As new findings, we report the following: (1) The system is more likely to fall into an unbalanced state when multiple enterprises adopt the policy of dynamic output adjustment simultaneously. (2) Enterprises with large output and small output have different output adjustment policies. When enterprises with big-scale output adopt a bit larger adjustment policies, enterprises with small output will be strongly impacted, and the available adjustment space will be sharply compressed. (3) The gradual increase in the difference between products reduces the stability of the market. (4) When product differentiation and bounded rationality strategies coexist, the steel market may fall into an unbalanced state when the degree of product difference increases excessively and the enterprise adopts more drastic output adjustment policies. Therefore, there are pros and cons to product differentiation strategy and bounded rationality adjustment strategy. When each steel oligopoly enterprise formulates a production plan, it needs to comprehensively consider the output changes of the other enterprises and carefully weigh the strategic issues.

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“…Li and Ma [10] considered a small rational dual-channel game and simulate their model's complex dynamic behaviour in their research. Many researchers have explored the complex dynamical behaviours of this type of models from different aspects, such as differentiated goods [11][12][13][14][15], bounded rationality [16], heterogeneous firms [7,[17][18][19], delayed decisions [20][21][22][23][24][25] and other factors [26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

et al. 2020

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The aim of this study is to analyse a discrete-time two-stage game with R&D competition by considering a continuous-time set-up with fixed delays. The model is represented in the form of delay differential equations. The stability of all the equilibrium points is studied. It is found that the model exhibits very complex dynamical behaviours, and its Nash equilibrium is destabilised via Hopf bifurcations.

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Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation

Cited by 56 publications

References 29 publications

The coevolution of the firm and the product attribute space

The coevolution of the firm and the product attribute space

Research on the Influence of Bounded Rationality and Product Differentiation on the Stability of Steel Industry Market

Bifurcation Analysis of a Duopoly Game with R&D Spillover, Price Competition and Time Delays

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