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Markov Perfect Equilibria in Differential Games with Regime Switching Strategies

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

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.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 4662.

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Date of creation: 2014
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Handle: RePEc:ces:ceswps:_4662
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  1. van der Ploeg, Frederick & Rohner, Dominic, 2012. "War and natural resource exploitation," European Economic Review, Elsevier, vol. 56(8), pages 1714-1729.
  2. Aaron Tornell, 1995. "Economic Growth and Decline with Endogenous Property Rights," Harvard Institute of Economic Research Working Papers 1739, Harvard - Institute of Economic Research.
  3. Frederick van der Ploeg, 2008. "Voracious Transformation of a Common Natural Resource into Productive Capital," OxCarre Working Papers 002, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  4. 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.
  5. repec:cup:cbooks:9780521855266 is not listed on IDEAS
  6. BOUCEKKINE, Raouf & KRAWCZYK, Jacek B. & VALLEE, Thomas, . "Environmental quality versus economic performance: a dynamic game approach," CORE Discussion Papers RP -2335, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Valente, Simone, 2011. "Endogenous Growth, Backstop Technology Adoption, And Optimal Jumps," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 293-325, June.
  8. BOUCEKKINE, RAOUF & SAGLAM , Cagri & VALLÉE, Thomas, 2003. "Technology adoption under embodiment: a two-stage optimal control approach," CORE Discussion Papers 2003055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Boucekkine, R. & Pommeret, A. & Prieur, F., 2013. "Optimal regime switching and threshold effects," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2979-2997.
  10. Fabien Prieur & Mabel Tidball & Cees Withagen, 2012. "Optimal Emission-Extraction Policy in a World of Scarcity and Irreversibility," OxCarre Working Papers 077, Oxford Centre for the Analysis of Resource Rich Economies, University of Oxford.
  11. 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.
  12. Fudenberg, Drew & Tirole, Jean, 1985. "Preemption and Rent Equilization in the Adoption of New Technology," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 383-401, July.
  13. Ngo Long, 2011. "Dynamic Games in the Economics of Natural Resources: A Survey," Dynamic Games and Applications, Springer, vol. 1(1), pages 115-148, March.
  14. Reinganum, Jennifer F., . "On the Diffusion of New Technology: A Game Theoretic Approach," Working Papers 312, California Institute of Technology, Division of the Humanities and Social Sciences.
  15. Alvarez-Cuadrado, Francisco & Van Long, Ngo, 2011. "Relative consumption and renewable resource extraction under alternative property-rights regimes," Resource and Energy Economics, Elsevier, vol. 33(4), pages 1028-1053.
  16. Daron Acemoglu & James A. Robinson, 2006. "Persistence of Power, Elites and Institutions," NBER Working Papers 12108, National Bureau of Economic Research, Inc.
  17. repec:cor:louvrp:2335 is not listed on IDEAS
  18. Makris, Miltiadis, 2001. "Necessary conditions for infinite-horizon discounted two-stage optimal control problems," Journal of Economic Dynamics and Control, Elsevier, vol. 25(12), pages 1935-1950, December.
  19. Tomiyama, Ken, 1985. "Two-stage optimal control problems and optimality conditions," Journal of Economic Dynamics and Control, Elsevier, vol. 9(3), pages 317-337, November.
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