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A dynamic conjectural variations model in the private provision of public goods: a differential game approach


  • Itaya, Jun-ichi
  • Shimomura, Koji


The purpose of this paper is to provide reasonable microfoundation to justify the concept of a conjectural valuations equilibrium which is often used in the literature on the private provision of public goods by incorporating an explicit dynamic process of learning with the help of the differential game. By interpreting the steady state conjectures in such a dynamic provision game as the conjectural variations variations in the corresponding static game, we derive zero or nonzero conjectural variations as an outcome of a learning process. Furthermore, we find that there may be uncountable conjectural variations and the possibility of matching behavior (i.e., positive conjectures), when nonlinear feedback strategies are available and when the domain of a state variable is appropriately restricted.
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Suggested Citation

  • Itaya, Jun-ichi & Shimomura, Koji, 2001. "A dynamic conjectural variations model in the private provision of public goods: a differential game approach," Journal of Public Economics, Elsevier, vol. 81(1), pages 153-172, July.
  • Handle: RePEc:eee:pubeco:v:81:y:2001:i:1:p:153-172

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    References listed on IDEAS

    1. Itaya, Jun-ichi & Dasgupta, Dipankar, 1995. "Dynamics, Consistent Conjectures, and Heterogeneous Agents in the Private Provision of Public Goods," Public Finance = Finances publiques, , vol. 50(3), pages 371-389.
    2. Fershtman, Chaim & Nitzan, Shmuel, 1991. "Dynamic voluntary provision of public goods," European Economic Review, Elsevier, vol. 35(5), pages 1057-1067, July.
    3. Cornes, Richard & Sandler, Todd, 1985. "On the consistency of conjectures with public goods," Journal of Public Economics, Elsevier, vol. 27(1), pages 125-129, June.
    4. Bergstrom, Theodore & Blume, Lawrence & Varian, Hal, 1986. "On the private provision of public goods," Journal of Public Economics, Elsevier, vol. 29(1), pages 25-49, February.
    5. Scafuri, Allen J., 1988. "On consistency of conjectures in the private provision of public goods," Journal of Public Economics, Elsevier, vol. 37(3), pages 395-398, December.
    6. Costrell, Robert M., 1991. "Immiserizing growth with semi-public goods under consistent conjectures," Journal of Public Economics, Elsevier, vol. 45(3), pages 383-389, August.
    7. Shimomura, Koji, 1991. "The feedback equilibria of a differential game of capitalism," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 317-338, April.
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    Cited by:

    1. 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.
    2. Akihiko Yanase, 2006. "Dynamic Voluntary Provision of Public Goods and Optimal Steady-State Subsidies," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 8(1), pages 171-179, January.
    3. Fujiwara, Kenji, 2008. "Duopoly can be more anti-competitive than monopoly," Economics Letters, Elsevier, vol. 101(3), pages 217-219, December.
    4. Figuieres, Charles & Tidball, Mabel & Jean-Marie, Alain, 2004. "On the effects of conjectures in a symmetric strategic setting," Research in Economics, Elsevier, vol. 58(1), pages 75-102, March.
    5. Fujiwara, Kenji, 2011. "Losses from competition in a dynamic game model of a renewable resource oligopoly," Resource and Energy Economics, Elsevier, vol. 33(1), pages 1-11, January.
    6. John Heywood & Zheng Wang, 2016. "Consistent location conjectures under spatial price discrimination," Journal of Economics, Springer, vol. 117(2), pages 167-180, March.
    7. 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.
    8. L. Lambertini, 2017. "Regulating the tragedy of commons: nonlinear feedback solutions of a differential game with a dual interpretation," Working Papers wp1096, Dipartimento Scienze Economiche, Universita' di Bologna.
    9. 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.
    10. Shaffer, Sherrill & Shogren, Jason F., 2009. "Repeated contests: A general parameterization," Economics Letters, Elsevier, vol. 105(2), pages 159-161, November.
    11. 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.
    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. Charles Figuières, 2009. "Markov interactions in a class of dynamic games," Theory and Decision, Springer, vol. 66(1), pages 39-68, January.
    14. Ngo Van Long & Koji Shimomura, 2006. "Voluntary Contributions to a Public Good: Non-neutrality Results / Contributions volontaires, biens publics," CIRANO Working Papers 2006s-20, CIRANO.
    15. Katsuhiko Hori & Akihisa Shibata, 2008. "A Dynamic Game Model of Endogenous Growth with Consumption Externalities," Keio/Kyoto Joint Global COE Discussion Paper Series 2008-040, Keio/Kyoto Joint Global COE Program.
    16. Marco Battaglini & Salvatore Nunnari & Thomas Palfrey, 2011. "The Free Rider Problem: a Dynamic Analysis," Working Papers 1354, Princeton University, Department of Economics, Econometric Research Program..
    17. Laura Marsiliani & Thomas I. Renstroem, 2010. "Privately provided public goods in a dynamic economy," Working Papers 2010_02, Durham University Business School.
    18. Luisito Bertinelli & Amer Tabakovic & Luca Marchiori & Benteng Zou, 2015. "Transboundary Pollution Abatement: The Impact of Unilateral Commitment in Differential Games," CREA Discussion Paper Series 15-02, Center for Research in Economic Analysis, University of Luxembourg.
    19. 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).
    20. repec:eee:ecmode:v:68:y:2018:i:c:p:409-415 is not listed on IDEAS
    21. 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.
    22. repec:eee:apmaco:v:270:y:2015:i:c:p:505-510 is not listed on IDEAS
    23. John Heywood & Guangliang Ye, 2010. "Optimal privatization in a mixed duopoly with consistent conjectures," Journal of Economics, Springer, vol. 101(3), pages 231-246, November.

    More about this item

    JEL classification:

    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods
    • F13 - International Economics - - Trade - - - Trade Policy; International Trade Organizations
    • D62 - Microeconomics - - Welfare Economics - - - Externalities


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