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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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    More about this item

    Keywords

    Differential games; Regime switching strategies; Technology adoption; Non-renewable resources;

    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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