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Piecewise closed-loop equilibria in differential games with regime switching strategies

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  • Long, Ngo Van
  • Prieur, Fabien
  • Tidball, Mabel
  • Puzon, Klarizze

Abstract

We propose a new methodology exploring piecewise closed-loop equilibrium strategies in differential games with regime switching actions. We develop a general game with two players. Players choose an action that influences the evolution of a state variable, and decide on the switching time from one regime to another. Compared to the optimal control problem with regime switching, necessary optimality conditions are modified for the first player to switch. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player’s actions and consequently on her own payoffs. In order to determine the equilibrium timing of regime changes, we derive conditions that help eliminate candidate equilibrium strategies that do not survive deviations in switching strategies. We then apply this new methodology to an exhaustible resource extraction game.

Suggested Citation

  • Long, Ngo Van & Prieur, Fabien & Tidball, Mabel & Puzon, Klarizze, 2017. "Piecewise closed-loop equilibria in differential games with regime switching strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 76(C), pages 264-284.
    • Handle: RePEc:eee:dyncon:v:76:y:2017:i:c:p:264-284
    DOI: 10.1016/j.jedc.2017.01.008
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    Cited by:

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    2. Anton Bondarev, 2021. "Games Without Winners: Catching-up with Asymmetric Spillovers," Dynamic Games and Applications, Springer, vol. 11(4), pages 670-703, December.
    3. Weihao Wang & Deqing Ma & Jinsong Hu, 2023. "Study of Carbon Reduction and Marketing Decisions with the Envisioning of a Favorable Event under Cap-and-Trade Regulation," IJERPH, MDPI, vol. 20(5), pages 1-27, March.
    4. Seidl, Andrea, 2019. "Zeno points in optimal control models with endogenous regime switching," Journal of Economic Dynamics and Control, Elsevier, vol. 100(C), pages 353-368.
    5. Carles Mañó-Cabello & Jesús Marín-Solano & Jorge Navas, 2021. "A Resource Extraction Model with Technology Adoption under Time Inconsistent Preferences," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    6. Gezer, Serhat, 2019. "Delaying product introduction: A dynamic analysis with endogenous time horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 102(C), pages 96-114.

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    More about this item

    Keywords

    Differential games; Regime switching strategies; Technology adoption; Non-renewable resources;
    All these keywords.

    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
    • Q32 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - Exhaustible Resources and Economic Development

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