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Games without winners: Catching-up with asymmetric spillovers

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  • Bondarev, Anton

Abstract

Dynamic game with changing leader is studied on the example of R&D co-opetition structure. The leader benefits from higher followers' innovations rate and followers are enjoying a spillover from the leader. Leadership changes because of asymmetric efficiency of investments of players. It is demonstrated that under sufficiently asymmetric players there is no long-run leader in this game and all players act as followers. Moreover this outcome may be the socially optimal one. In decentralised setting additional complex types of dynamics are observed: permanent uctuations around symmetric (pseudo)equilibrium and chaotic dynamics. This last is possible only once strategies of players are interdependent. Cooperative solution is qualitatively similar for any number of players while market solution is progressively complex given all players are asymmetric. Results are extended to an arbitrary linear-quadratic multi-modal differential game with spillovers and the structure necessary for the onset of non-deterministic chaos is discussed.

Suggested Citation

  • Bondarev, Anton, 2018. "Games without winners: Catching-up with asymmetric spillovers," Working papers 2018/12, Faculty of Business and Economics - University of Basel.
  • Handle: RePEc:bsl:wpaper:2018/12
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    References listed on IDEAS

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    1. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    2. Bondarev, Anton, 2014. "Endogenous specialization of heterogeneous innovative activities of firms under the technological spillovers," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 235-249.
    3. Motta, Massimo & Thisse, Jacques-Francois & Cabrales, Antonio, 1997. "On the Persistence of Leadership or Leapfrogging in International Trade," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(4), pages 809-824, November.
    4. Greiner, Alfred & Bondarev, Anton, 2017. "Optimal R&D investment with learning-by-doing: Multiple steady-states and thresholds," Working papers 2017/06, Faculty of Business and Economics - University of Basel.
    5. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329.
    6. Gnyawali, Devi R. & Park, Byung-Jin (Robert), 2011. "Co-opetition between giants: Collaboration with competitors for technological innovation," Research Policy, Elsevier, vol. 40(5), pages 650-663, June.
    7. Dawid, H. & Kopel, M. & Kort, P.M., 2013. "R&D competition versus R&D cooperation in oligopolistic markets with evolving structure," International Journal of Industrial Organization, Elsevier, vol. 31(5), pages 527-537.
    8. Anton Bondarev, 2016. "Intensity of R&D competition and the generation of innovations in heterogeneous setting," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 621-653, July.
    9. Petrosjan, Leon & Zaccour, Georges, 2003. "Time-consistent Shapley value allocation of pollution cost reduction," Journal of Economic Dynamics and Control, Elsevier, vol. 27(3), pages 381-398, January.
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    More about this item

    Keywords

    technological spillovers; heterogeneous innovations; asymmetric players; social optimality; market inefficiency; multi-modal differential games; piecewise-smooth systems;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • L16 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Industrial Organization and Macroeconomics; Macroeconomic Industrial Structure
    • O32 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights - - - Management of Technological Innovation and R&D

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