R&amp;D games in a Cournot duopoly with isoelastic demand functions: A comment

Luckraz, Shravan

doi:10.1016/j.econmod.2011.07.019

Cited by 10 publications

(6 citation statements)

References 10 publications

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“…e profit function about R&D efforts x i captured by taking equation (6) into equation (4) in reverse order can be obtained as…”

Section: The Modelmentioning

confidence: 99%

“…Proof. e corresponding discriminant of roots of characteristic polynomial (23) is given as 6 Complexity…”

Section: □ Propositionmentioning

confidence: 99%

“…Based on this assumption, D'Aspremont and Jacquemin [5] built the foundation of the performance of R&D cooperation in the product differentiation market. Luckraz [6] established a Cournot duopoly game model with isoelastic demand function and also considered the case without R&D spillovers. e work of Chatterjee [7] showed that the firms in the market undertake R&D activity and studied that R&D incentive may depend on the information structures they had.…”

Section: Introductionmentioning

confidence: 99%

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A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

Zhou

Chu

et al. 2020

Complexity

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In this paper, a dynamic two-stage Cournot duopoly game with R&D efforts is built. Then, the local stability of the equilibrium points are discussed, and the stability condition of the Nash equilibrium point is also deduced through Jury criterion. The complex dynamical behaviors of the built model are investigated by numerical simulations. We found that the unique route to chaos is flip bifurcation, and the increase of adjusting speed will cause the system to lose stability and produce more complex dynamic behavior. In addition, we also found the phenomenon of multistability in the given model. Several kinds of coexistence of attractors are shown. In particular, we found that boundary attractors can coexist with internal attractors, which also aggravates the complexity of the system. At last, the chaotic state in the built system has been successfully controlled.

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“…e profit function about R&D efforts x i captured by taking equation (6) into equation (4) in reverse order can be obtained as…”

Section: The Modelmentioning

confidence: 99%

“…Proof. e corresponding discriminant of roots of characteristic polynomial (23) is given as 6 Complexity…”

Section: □ Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

Zhou

Chu

et al. 2020

Complexity

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“…Fabra and Garcia [13] studied the relationship between dynamic price competition and cost transformation. Luckraz [31] studied R&D game in a Cournot duopoly with isoelastic demand functions. In the work of Bondarev and Greiner [5], learning functions were introduced to analyze the relationship between the dynamic leadership of leader and follower.…”

mentioning

confidence: 99%

Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition

Liu¹,

Liu²,

Xu³

2023

JIMO

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<p style='text-indent:20px;'>The importance of knowledge and technology is self-evident, especially the core technology of key nodes in the industrial chain, which will change the country's status in the supply chain, and even the national economic security. This scenario has led to a global non-cooperative innovation competition. In order to ensure the safety of local industrial chain and shorten the technological distance with developed countries, emerging economies can adopt imitative innovation by observing the core technologies from developed countries, or choose independent innovation strategy. How should emerging economies make the choice? We analyze this problem by establishing a dynamic non-cooperative technology development model. The research results show that when the innovation capacity gap between emerging economies and developed regions is large, the choice of imitation strategy is highly necessary. And when the gap is small, the independent innovation strategy can be selected. In addition, due to the existence of both domestic and foreign markets, developed countries can adopt strict policies to restrict the sale of products containing core technologies to overseas markets to limit the spillover of important technologies. We also consider the impact of policies that limit technology spillovers and show the impact of local market capacity in emerging economies.</p>

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“…Petit and Sanna-Randaccio [6] considered a two-country imperfect competition model and examined the influence of the firms mode of foreign expansion on the incentive innovation as well as the impact of R&D activities and technological spillovers on the international strategy. Luckraz [7] showed a note in a two-stage Cournot R&D game model with isoelastic demand functions. Luckraz [8] demonstrated innovation (or Schumpeter's) cycles in a discrete and finite dynamic game of innovation and imitation and concluded that strategic interactions were sufficient to generate cycles.…”

Section: Introductionmentioning

confidence: 99%

Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

Zhan

Mao

2017

Discrete Dynamics in Nature and Society

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We study a dynamic research and development two-stage input competition game model in the Bertrand duopoly oligopoly market with spillover effects on cost reduction. We investigate the stability of the Nash equilibrium point and local stable conditions and stability region of the Nash equilibrium point by the bifurcation theory. The complex dynamic behaviors of the system are shown by numerical simulations. It is demonstrated that chaos occurs for a range of managerial policies, and the associated unpredictability is solely due to the dynamics of the interaction. We show that the straight line stabilization method is the appropriate management measure to control the chaos.

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R&D games in a Cournot duopoly with isoelastic demand functions: A comment

Cited by 10 publications

References 10 publications

A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

A Dynamic Duopoly Cournot Model with R&D Efforts and Its Dynamic Behavior Analysis

Imitative innovation or independent innovation strategic choice of emerging economies in non-cooperative innovation competition

Complex Dynamics and Chaos Control on a Kind of Bertrand Duopoly Game Model considering R&D Activities

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