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Optimal switching from competition to cooperation: a preliminary exploration

Author

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  • 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 Panthéon-Sorbonne - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - 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)

  • Benteng Zou

    () (University of Luxembourg [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 the- oretical 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, 2021. "Optimal switching from competition to cooperation: a preliminary exploration," Post-Print hal-02950698, HAL.
  • Handle: RePEc:hal:journl:hal-02950698
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-02950698
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    References listed on IDEAS

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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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