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Markov Perfect Equilibria in Differential Games with Regime Switching Strategies

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Listed:
  • Ngo Van Long
  • Fabien Prieur
  • Klarizze Puzon
  • Mabel Tidball

Abstract

We propose a new methodology exploring Markov perfect equilibrium strategies in differential games with regime switching. Specifically, we develop a general game with two players having two kinds of strategies. 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-mover. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player’s actions and payoffs. In order to determine the equilibrium timing of regime changes, the notion of wrong timing is introduced and necessary conditions for a particular timing to be wrong are derived. We then apply this new methodology to an exhaustible resource extraction game. Sufficient conditions for the existence of an interior solution are compared to those characterizing a wrong timing. The impact of feedback strategies for the equilibrium adoption time depends on the balance between two conflicting effects: the first mover incurs an indirect cost due to the future switching of her rival (incentive to delay the switch). But she is able to affect the other player’s switching decision (incentive to switch more rapidly). In a particular case without direct switching cost, the interplay between the two ensures that the first-mover adopts the new technology in finite time. Interestingly, this result differs from what is obtained in a non-game theoretic framework, i.e. immediate adoption.

Suggested Citation

  • Ngo Van Long & Fabien Prieur & Klarizze Puzon & Mabel Tidball, 2014. "Markov Perfect Equilibria in Differential Games with Regime Switching Strategies," CESifo Working Paper Series 4662, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_4662
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    References listed on IDEAS

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    1. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2013. "Technological vs. Ecological Switch and the Environmental Kuznets Curve," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 95(2), pages 252-260.
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    5. Raouf Boucekkine & Aude Pommeret & Fabien Prieur, 2012. "Optimal Regime Switching and Threshold Effects: Theory and Application to a Resource Extraction Problem under Irreversibility," Working Papers halshs-00793200, HAL.
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    Cited by:

    1. Dmitry Gromov & Ekaterina Gromova, 2017. "On a Class of Hybrid Differential Games," Dynamic Games and Applications, Springer, vol. 7(2), pages 266-288, June.
    2. Raouf Boucekkine & Fabien Prieur & Klarizze Puzon, 2014. "On the Timing of Political Regime Changes: Theory and Application to the Arab Spring," Working Papers 2014.104, Fondazione Eni Enrico Mattei.

    More about this item

    Keywords

    differential games; regime switching; 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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