IDEAS home Printed from https://ideas.repec.org/a/spr/dyngam/v8y2018i3d10.1007_s13235-018-0257-7.html
   My bibliography  Save this article

Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games

Author

Listed:
  • Javier Frutos

    (Universidad de Valladolid)

  • Guiomar Martín-Herrán

    (Universidad de Valladolid)

Abstract

This paper revisits the problem of how to select an equilibrium in a differential game in the case of multiplicity of Nash equilibria. Most of the previous applied dynamic games literature has considered pre-play negotiations between players, implicitly or explicitly, with the aim of reaching an agreement on the selection of the pair of strategies. The main objective of this paper is to determine what would be the equilibrium to be played without pre-play communications. We study the linear and nonlinear Markov perfect Nash equilibria for a class of well-known models in the literature if pre-play communications are eliminated. We analyze both symmetric and nonsymmetric strategies. We show that the nonlinear strategies are not always the optimal strategies implemented when pre-play communications are removed. We conclude that in the presence of multiple equilibria and without pre-play communications the equilibria actually implemented are symmetric piecewise linear Markov perfect Nash equilibria at least for a range of initial values of the state variable.

Suggested Citation

  • Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.
    • Handle: RePEc:spr:dyngam:v:8:y:2018:i:3:d:10.1007_s13235-018-0257-7
    DOI: 10.1007/s13235-018-0257-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13235-018-0257-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13235-018-0257-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kenji Fujiwara, 2009. "Why Environmentalists Resist Trade Liberalization," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 44(1), pages 71-84, September.
    2. Benchekroun, Hassan & Long, Ngo Van, 2008. "The build-up of cooperative behavior among non-cooperative selfish agents," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 239-252, July.
    3. Wirl, Franz & Dockner, Engelbert, 1995. "Leviathan governments and carbon taxes: Costs and potential benefits," European Economic Review, Elsevier, vol. 39(6), pages 1215-1236, June.
    4. Tsutsui, Shunichi & Mino, Kazuo, 1990. "Nonlinear strategies in dynamic duopolistic competition with sticky prices," Journal of Economic Theory, Elsevier, vol. 52(1), pages 136-161, October.
    5. Chiarella, Carl, et al, 1984. "On the Economics of International Fisheries," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 85-92, February.
    6. 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.
    7. Zagonari, Fabio, 1998. "International Pollution Problems: Unilateral Initiatives by Environmental Groups in One Country," Journal of Environmental Economics and Management, Elsevier, vol. 36(1), pages 46-69, July.
    8. Santiago Rubio & Begoña Casino, 2003. "Strategic Behavior and Efficiency in the Common Property Extraction of Groundwater," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 26(1), pages 73-87, September.
    9. Ihori, Toshihiro & Itaya, Jun-ichi, 2001. "A dynamic model of fiscal reconstruction," European Journal of Political Economy, Elsevier, vol. 17(4), pages 779-797, November.
    10. 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.
    11. Piga, Claudio A. G., 2000. "Competition in a duopoly with sticky price and advertising," International Journal of Industrial Organization, Elsevier, vol. 18(4), pages 595-614, May.
    12. Dockner, Engelbert J. & Sorger, Gerhard, 1996. "Existence and Properties of Equilibria for a Dynamic Game on Productive Assets," Journal of Economic Theory, Elsevier, vol. 71(1), pages 209-227, October.
    13. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    14. Rincon-Zapatero, J. P., 2004. "Characterization of Markovian equilibria in a class of differential games," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1243-1266, April.
    15. Dockner Engelbert J. & Van Long Ngo, 1993. "International Pollution Control: Cooperative versus Noncooperative Strategies," Journal of Environmental Economics and Management, Elsevier, vol. 25(1), pages 13-29, July.
    16. Kenji Fujiwara, 2010. "When Are Voluntary Export Restraints Voluntary? A Differential Game Approach," Australian Economic Papers, Wiley Blackwell, vol. 49(2), pages 101-110, June.
    17. Wirl, Franz, 1996. "Dynamic voluntary provision of public goods: Extension to nonlinear strategies," European Journal of Political Economy, Elsevier, vol. 12(3), pages 555-560, November.
    18. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
    19. Kossioris, G. & Plexousakis, M. & Xepapadeas, A. & de Zeeuw, A. & Mäler, K.-G., 2008. "Feedback Nash equilibria for non-linear differential games in pollution control," Journal of Economic Dynamics and Control, Elsevier, vol. 32(4), pages 1312-1331, April.
    20. repec:bla:econom:v:69:y:2002:i:273:p:93-111 is not listed on IDEAS
    21. P. Cartigny & P. Michel, 2003. "On the Selection of One Feedback Nash Equilibrium in Discounted Linear-Quadratic Games," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 231-243, May.
    22. 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.
    23. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, vol. 24(3), pages 251-261, June.
    24. repec:bla:econom:v:64:y:1997:i:253:p:137-54 is not listed on IDEAS
    25. Feichtinger, Gustav & Wirl, Franz, 1993. "A Dynamic Variant of the Battle of the Sexes," International Journal of Game Theory, Springer;Game Theory Society, vol. 22(4), pages 359-380.
    26. Javier Frutos & Guiomar Martín-Herrán, 2015. "Does Flexibility Facilitate Sustainability of Cooperation Over Time? A Case Study from Environmental Economics," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 657-677, May.
    27. Dockner, Engelbert J. & Van Long, Ngo & Sorger, Gerhard, 1996. "Analysis of Nash equilibria in a class of capital accumulation games," Journal of Economic Dynamics and Control, Elsevier, vol. 20(6-7), pages 1209-1235.
    28. Kenji Fujiwara & Norimichi Matsueda, 2009. "Dynamic Voluntary Provision of Public Goods: A Generalization," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 11(1), pages 27-36, February.
    29. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, November.
    30. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    31. Akihisa Shibata, 2002. "Strategic Interactions in a Growth Model with Infrastructure Capital," Metroeconomica, Wiley Blackwell, vol. 53(4), pages 434-460, November.
    32. Wirl Franz, 1994. "Pigouvian Taxation of Energy for Flow and Stock Externalities and Strategic, Noncompetitive Energy Pricing," Journal of Environmental Economics and Management, Elsevier, vol. 26(1), pages 1-18, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Steffen Jørgensen & Ngo Long & Gerhard Sorger, 2018. "Preface: Special issue of Dynamic Games and Applications in Memory of Professor Engelbert J. Dockner," Dynamic Games and Applications, Springer, vol. 8(3), pages 457-467, September.
    2. Javier Frutos & Víctor Gatón & Paula M. López-Pérez & Guiomar Martín-Herrán, 2022. "Investment in Cleaner Technologies in a Transboundary Pollution Dynamic Game: A Numerical Investigation," Dynamic Games and Applications, Springer, vol. 12(3), pages 813-843, September.
    3. Niko Jaakkola & Florian Wagener, 2020. "All symmetric equilibria in differential games with public goods," Tinbergen Institute Discussion Papers 20-020/II, Tinbergen Institute.
    4. Niko Jaakkola & Florian Wagener & Florian O.O. Wagener, 2023. "Differential Games of Public Investment," CESifo Working Paper Series 10585, CESifo.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Rowat, Colin, 2007. "Non-linear strategies in a linear quadratic differential game," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3179-3202, October.
    3. Santiago J. Rubio, 2002. "On The Coincidence Of The Feedback Nash And Stackelberg Equilibria In Economic Applications Of Differential Games," Working Papers. Serie AD 2002-11, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Calvo, Emilio & Rubio, Santiago J., 2013. "Dynamic Models of International Environmental Agreements: A Differential Game Approach," International Review of Environmental and Resource Economics, now publishers, vol. 6(4), pages 289-339, April.
    5. 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.
    6. Fouad El Ouardighi & Konstantin Kogan & Giorgio Gnecco & Marcello Sanguineti, 2020. "Transboundary pollution control and environmental absorption efficiency management," Annals of Operations Research, Springer, vol. 287(2), pages 653-681, April.
    7. Lambertini, Luca, 2021. "Regulating the tragedy of commons: Nonlinear feedback solutions of a differential game with a dual interpretation," Energy Economics, Elsevier, vol. 100(C).
    8. Rémy Dullieux & Lionel Ragot & Katheline Schubert, 2011. "Carbon Tax and OPEC’s Rents Under a Ceiling Constraint," Scandinavian Journal of Economics, Wiley Blackwell, vol. 113(4), pages 798-824, December.
    9. Bård Harstad, 2016. "The Dynamics Of Climate Agreements," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 719-752, June.
    10. 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.
    11. Niko Jaakkola & Florian Wagener & Florian O.O. Wagener, 2023. "Differential Games of Public Investment," CESifo Working Paper Series 10585, CESifo.
    12. Eggert, Wolfgang & Itaya, Jun-ichi & Mino, Kazuo, 2011. "A dynamic model of conflict and appropriation," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1), pages 167-182.
    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. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    15. Rubio, Santiago J. & Casino, Begona, 2002. "A note on cooperative versus non-cooperative strategies in international pollution control," Resource and Energy Economics, Elsevier, vol. 24(3), pages 251-261, June.
    16. 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.
    17. Johannes M. Schumacher & Puduru Viswanadha Reddy & Jacob C. Engwerda, 2022. "Jump Equilibria in Public-Good Differential Games with a Single State Variable," Dynamic Games and Applications, Springer, vol. 12(3), pages 784-812, September.
    18. Athanassoglou, Stergios, 2010. "Dynamic nonpoint-source pollution control policy: Ambient transfers and uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 34(12), pages 2494-2509, December.
    19. Akihiko Yanase & Keita Kamei, 2022. "Dynamic Game of International Pollution Control with General Oligopolistic Equilibrium: Neary Meets Dockner and Long," Dynamic Games and Applications, Springer, vol. 12(3), pages 751-783, September.
    20. K. Hori & A. Shibata, 2010. "Dynamic Game Model of Endogenous Growth with Consumption Externalities," Journal of Optimization Theory and Applications, Springer, vol. 145(1), pages 93-107, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:dyngam:v:8:y:2018:i:3:d:10.1007_s13235-018-0257-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.