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Optimal switching from competition to cooperation: a preliminary exploration

Author

Listed:
  • Raouf Boucekkine

    () (Aix-Marseille University, CNRS and EHESS)

  • Carmen Camacho

    () (Paris School of Economics, CNRS)

  • Benteng Zou

    () (CREA, Université du Luxembourg)

Abstract

In this paper, we tackle a generic optimal regime switching problem where the decision making process is not the same from a regime to another. Precisely, we consider a simple model of optimal switching from competition to cooperation. To this end, we solve a two- stage optimal control problem. In the first stage, two players engage in a dynamic game with a common state variable and one control for each player. We solve for open-loop strategies with a linear state equation and linear-quadratic payoffs. More importantly, the players may also consider the possibility to switch at finite time to a cooperative regime with the associated joint optimization of the sum of the individual payoffs. Using theoretical analysis and numerical exercises, we study the optimal switching strategy from competition to cooperation. We also discuss the reverse switching.

Suggested Citation

  • Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2020. "Optimal switching from competition to cooperation: a preliminary exploration," CREA Discussion Paper Series 20-02, Center for Research in Economic Analysis, University of Luxembourg.
  • Handle: RePEc:luc:wpaper:20-02
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    References listed on IDEAS

    as
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    2. Boucekkine, R. & Pommeret, A. & Prieur, F., 2013. "Optimal regime switching and threshold effects," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2979-2997.
    3. Boucekkine, Raouf & Saglam, Cagri & Vallã©Ee, Thomas, 2004. "Technology Adoption Under Embodiment: A Two-Stage Optimal Control Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 8(2), pages 250-271, April.
    4. Zampolli, Fabrizio, 2006. "Optimal monetary policy in a regime-switching economy: The response to abrupt shifts in exchange rate dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1527-1567.
    5. Tsur, Yacov & Zemel, Amos, 2003. "Optimal transition to backstop substitutes for nonrenewable resources," Journal of Economic Dynamics and Control, Elsevier, vol. 27(4), pages 551-572, February.
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    11. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, 2011. "Environmental quality versus economic performance: a dynamic game approach," CORE Discussion Papers RP 2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    More about this item

    Keywords

    Cooperation; competition; dynamic games; multi-stage optimal control.;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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