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Optimal switching from competition to cooperation: a preliminary exploration

Author

Listed:
  • Raouf Boucekkine

    (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique)

  • Carmen Camacho

    (PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Benteng Zou

    (uni.lu - Université du Luxembourg = University of Luxembourg = Universität Luxemburg)

Abstract

In this paper, we tackle a generic optimal regime switching problem where the decision-making process is not the same from one 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 reverse switching.

Suggested Citation

  • Raouf Boucekkine & Carmen Camacho & Benteng Zou, 2021. "Optimal switching from competition to cooperation: a preliminary exploration," Post-Print hal-02950698, HAL.
    • Handle: RePEc:hal:journl:hal-02950698
    DOI: 10.1007/978-3-030-54576-5_9
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    Cited by:

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    2. Boucekkine, Raouf & Ruan, Weihua & Zou, Benteng, 2023. "The irreversible pollution game," Journal of Environmental Economics and Management, Elsevier, vol. 120(C).
    3. Yutao Han & Zhen Song, 2022. "On regional integration, fiscal income, and GDP per capita," Scottish Journal of Political Economy, Scottish Economic Society, vol. 69(5), pages 506-532, November.
    4. Raouf Boucekkine & Carmen Camacho & Weihua Ruan & Benteng Zou, 2022. "Why and when coalitions split? An alternative analytical approach with an application to environmental agreements," Working Papers halshs-03676670, HAL.

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    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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