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New Method to Characterize Subgame Perfect Nash Equilibria in Differential Games

Author

Listed:
  • J. P. Rincón-Zapatero

    (Universidad de Valladolid)

  • J. Martínez

    (Universidad de Valladolid)

  • G. Martín-Herrán

    (Universidad de Valladolid)

Abstract

In this paper, we present a method for computing Nash equilibria in feedback strategies. This method gives necessary and sufficient conditions to characterize subgame perfect equilibria by means of a system of quasilinear partial differential equations. This characterization allows one to know explicitly the solution of the game in some cases. In other cases, this approach makes a qualitative study easier. We apply this method to nonrenewable resource games.

Suggested Citation

  • J. P. Rincón-Zapatero & J. Martínez & G. Martín-Herrán, 1998. "New Method to Characterize Subgame Perfect Nash Equilibria in Differential Games," Journal of Optimization Theory and Applications, Springer, vol. 96(2), pages 377-395, February.
    • Handle: RePEc:spr:joptap:v:96:y:1998:i:2:d:10.1023_a:1022674215872
    DOI: 10.1023/A:1022674215872
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    Cited by:

    1. Zaruhi Hakobyan & Christos Koulovatianos, 2021. "Symmetric Markovian Games of Commons with Potentially Sustainable Endogenous Growth," Dynamic Games and Applications, Springer, vol. 11(1), pages 54-83, March.
    2. Rouillon, Sébastien, 2013. "A simple characterization of the optimal extraction policy of a non-renewable resource when extraction cost is stock-independent," Energy Economics, Elsevier, vol. 37(C), pages 100-103.
    3. Engelbert Dockner & Florian Wagener, 2014. "Markov perfect Nash equilibria in models with a single capital stock," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(3), pages 585-625, August.
    4. Tasneem, Dina & Engle-Warnick, Jim & Benchekroun, Hassan, 2017. "An experimental study of a common property renewable resource game in continuous time," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 91-119.
    5. Sébastien Rouillon, 2017. "Cooperative and Noncooperative Extraction in a Common Pool with Habit Formation," Dynamic Games and Applications, Springer, vol. 7(3), pages 468-491, September.
    6. Colombo, Luca & Labrecciosa, Paola, 2015. "On the Markovian efficiency of Bertrand and Cournot equilibria," Journal of Economic Theory, Elsevier, vol. 155(C), pages 332-358.
    7. Wirl, Franz, 2007. "Do multiple Nash equilibria in Markov strategies mitigate the tragedy of the commons?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(11), pages 3723-3740, November.
    8. 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.

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