IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_10585.html
   My bibliography  Save this paper

Differential Games of Public Investment: Markovian Best Responses in the General Case

Author

Listed:
  • Niko Jaakkola
  • Florian Wagener
  • Florian O.O. Wagener

Abstract

We define a differential game of public investment with a discontinuous Markovian strategy space. The best response correspondence for the game is well-behaved: a best response exists and uniquely maps almost all profiles of opponents’ strategies back to the strategy space. Our chosen strategy space thus makes the differential game well-formed as a static game in Markovian strategies, resolving a long-standing open problem in the literature. We provide a user-friendly necessary and sufficient condition for constructing the best response. Our methods do not require specific functional forms. Our theory has general applications, including to problems of noncooperative control of stock pollutants, harvesting of natural resources, and joint investment problems.

Suggested Citation

  • Niko Jaakkola & Florian Wagener & Florian O.O. Wagener, 2023. "Differential Games of Public Investment: Markovian Best Responses in the General Case," CESifo Working Paper Series 10585, CESifo.
    • Handle: RePEc:ces:ceswps:_10585
    as

    Download full text from publisher

    File URL: https://www.cesifo.org/DocDL/cesifo1_wp10585.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Achdou, Yves & Han, Jiequn & Lasry, Jean Michel & Lions, Pierre Louis & Moll, Ben, 2022. "Income and wealth distribution in macroeconomics: a continuous-time approach," LSE Research Online Documents on Economics 107422, London School of Economics and Political Science, LSE Library.
    2. 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.
    3. Yves Achdou & Jiequn Han & Jean-Michel Lasry & Pierre-Louis Lionse & Benjamin Moll, 2022. "Income and Wealth Distribution in Macroeconomics: A Continuous-Time Approach [On the Existence and Uniqueness of Stationary Equilibrium in Bewley Economies with Production]," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 45-86.
    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. Brunnermeier, Markus & Sannikov, Yuliy, 2016. "Macro, Money and Finance: A Continuous Time Approach," CEPR Discussion Papers 11329, C.E.P.R. Discussion Papers.
    6. Skiba, A K, 1978. "Optimal Growth with a Convex-Concave Production Function," Econometrica, Econometric Society, vol. 46(3), pages 527-539, May.
    7. 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.
    8. 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.
    9. Frederick Ploeg & Aart Zeeuw, 1992. "International aspects of pollution control," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 2(2), pages 117-139, March.
    10. 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.
    11. Eduardo Faingold & Yuliy Sannikov, 2011. "Reputation in Continuous‐Time Games," Econometrica, Econometric Society, vol. 79(3), pages 773-876, May.
    12. 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.
    13. 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.
    14. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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).
    9. Niko Jaakkola & Florian Wagener, 2020. "All symmetric equilibria in differential games with public goods," Tinbergen Institute Discussion Papers 20-020/II, Tinbergen Institute.
    10. Ricardo Josa-Fombellida & Juan Rincón-Zapatero, 2015. "Euler–Lagrange equations of stochastic differential games: application to a game of a productive asset," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(1), pages 61-108, May.
    11. Bård Harstad, 2016. "The Dynamics Of Climate Agreements," Journal of the European Economic Association, European Economic Association, vol. 14(3), pages 719-752, June.
    12. Lambertini, Luca & Mantovani, Andrea, 2014. "Feedback equilibria in a dynamic renewable resource oligopoly: Pre-emption, voracity and exhaustion," Journal of Economic Dynamics and Control, Elsevier, vol. 47(C), pages 115-122.
    13. 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).
    14. Agnieszka Wiszniewska-Matyszkiel & Marek Bodnar & Fryderyk Mirota, 2015. "Dynamic Oligopoly with Sticky Prices: Off-Steady-state Analysis," Dynamic Games and Applications, Springer, vol. 5(4), pages 568-598, December.
    15. Lambertini, Luca & Mantovani, Andrea, 2016. "On the (in)stability of nonlinear feedback solutions in a dynamic duopoly with renewable resource exploitation," Economics Letters, Elsevier, vol. 143(C), pages 9-12.
    16. 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.
    17. Luca Lambertini, 2016. "Managerial Delegation in a Dynamic Renewable Resource Oligopoly," Dynamic Modeling and Econometrics in Economics and Finance, in: Herbert Dawid & Karl F. Doerner & Gustav Feichtinger & Peter M. Kort & Andrea Seidl (ed.), Dynamic Perspectives on Managerial Decision Making, pages 93-107, Springer.
    18. 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.
    19. Fouad El Ouardighi & Konstantin Kogan & Giorgio Gnecco & Marcello Sanguineti, 2018. "Commitment-Based Equilibrium Environmental Strategies Under Time-Dependent Absorption Efficiency," Group Decision and Negotiation, Springer, vol. 27(2), pages 235-249, April.
    20. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.

    More about this item

    Keywords

    differential games; Markov-perfect Nash equilibria; dynamic public investment;
    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
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:ces:ceswps:_10585. 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: Klaus Wohlrabe (email available below). General contact details of provider: https://edirc.repec.org/data/cesifde.html .

    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.