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A dynamic model of oligopoly with R&D externalities along networks. Part II

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  • Italo Bischi, Gian
  • Lamantia, Fabio

Abstract

In Bischi and Lamantia [4] a two-stage oligopoly game has been proposed to describe networks of firms that invest in cost-reducing R&D activity with the possibility of sharing R&D results with partner firms as well as gaining knowledge for free through spillovers, and an adaptive dynamic mechanism is proposed to describe how firms repeatedly update their R&D efforts over time. In that paper existence and stability of equilibria have been analyzed given a fixed structure of the collaboration network, divided into sub-networks. In this paper we analyze the influences of the degree of collaboration and spillovers on profits, social welfare and, more generally, on overall efficiency. We first consider two relevant benchmark cases, for which analytical results are provided, and then numerical experiments are performed to stress the role of the level of connectivity (i.e. the collaboration attitude) inside networks as well as the effects of involuntary knowledge spillovers inside each network and among different competing networks.

Suggested Citation

  • Italo Bischi, Gian & Lamantia, Fabio, 2012. "A dynamic model of oligopoly with R&D externalities along networks. Part II," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 66-82.
    • Handle: RePEc:eee:matcom:v:84:y:2012:i:c:p:66-82
    DOI: 10.1016/j.matcom.2012.09.001
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    1. Italo Bischi, Gian & Lamantia, Fabio, 2012. "A dynamic model of oligopoly with R&D externalities along networks. Part II," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 84(C), pages 66-82.
    2. Villena, Marcelo J. & Araneda, Axel A., 2017. "Dynamics and stability in retail competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 37-53.
    3. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
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    6. César García-Díaz & Gábor Péli & Arjen van Witteloostuijn, 2020. "The coevolution of the firm and the product attribute space," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-25, June.
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    9. Dawid, Herbert & Heitmann, Dennis, 2014. "Best response dynamics with level-n expectations in two-stage games," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 130-153.
    10. Cao, Yang & Colucci, Renato & Guerrini, Luca, 2022. "On the stability analysis of a delayed two-stage Cournot model with R&D spillovers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 543-554.
    11. Zhou, Jie & Zhou, Wei & Chu, Tong & Chang, Ying-xiang & Huang, Meng-jia, 2019. "Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 358-378.

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