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Comparing Open-Loop with Markov Equilibria in a Class of Differential Games

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  • Ngo Van Long
  • Koji Shimomura
  • Harutaka Takahashi

Abstract

We consider a class of differential games with transition equations that are homogeneous of degree one. For any game G with a discount rate r, consider a Markov perfect equilibrium (MPE) with strategies that are linear in the state variables. We show that the time paths of the control variables of this equilibrium constitute an open-loop equilibrium of a corresponding game Classification-JEL: C72; C73; Q30

Suggested Citation

  • Ngo Van Long & Koji Shimomura & Harutaka Takahashi, 1997. "Comparing Open-Loop with Markov Equilibria in a Class of Differential Games," CIRANO Working Papers 97s-22, CIRANO.
  • Handle: RePEc:cir:cirwor:97s-22
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    File URL: https://cirano.qc.ca/files/publications/97s-22.pdf
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    References listed on IDEAS

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    1. Clemhout, Simone & Wan, Henry Jr., 1994. "Differential games -- Economic applications," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 23, pages 801-825, Elsevier.
    2. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, January.
    3. Van Long, Ngo & Shimomura, Koji, 1998. "Some results on the Markov equilibria of a class of homogeneous differential games," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 557-566, January.
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    Cited by:

    1. Sébastien Rouillon, 2014. "Do Social Status Seeking Behaviors Worsen the Tragedy of the Commons?," Dynamic Games and Applications, Springer, vol. 4(1), pages 73-94, March.
    2. Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
    3. 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.
    4. Genc, Talat S. & De Giovanni, Pietro, 2018. "Optimal return and rebate mechanism in a closed-loop supply chain game," European Journal of Operational Research, Elsevier, vol. 269(2), pages 661-681.
    5. Talat S. Genc & Georges Zaccour, 2010. "Investment Dynamics: Good News Principle," Working Papers 1006, University of Guelph, Department of Economics and Finance.
    6. Murray C. Kemp & Ngo Van Long, 2007. "Development Aid in the Presence of Corruption: Differential Games among Donors," CIRANO Working Papers 2007s-23, CIRANO.
    7. Genc, Talat S., 2017. "The impact of lead time on capital investments," Journal of Economic Dynamics and Control, Elsevier, vol. 82(C), pages 142-164.
    8. Agah R. Turan, 2019. "Intentional time inconsistency," Theory and Decision, Springer, vol. 86(1), pages 41-64, February.
    9. Murray C. Kemp & Ngo Van Long, 2009. "Foreign Aid in the Presence of Corruption: Differential Games among Donors," Review of International Economics, Wiley Blackwell, vol. 17(SI), pages 230-243, May.

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    More about this item

    Keywords

    Differential games; Markov perfect equilibria; open-loop equilibria; Jeux différentiels; équilibre Markov-parfait; équilibre en boucle ouverte;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • Q30 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Nonrenewable Resources and Conservation - - - General

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