IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/509.html
   My bibliography  Save this paper

Perfect Uncontrollable Differential Games

Author

Listed:
  • R. Cellini
  • L. Lambertini
  • G. Leitmann

Abstract

This paper analyses the time consistency of open-loop equilibria, in the cases of Nash and Stackelberg behaviour. We define a class of games where the strong time-consistency of the open-loop Nash equilibrium associates with the time consistency of the open-loop Stackelberg equilibrium. We label these games as perfect uncontrollable . We provide one example based on a model of oligopolistic competition in advertising efforts. We also present two oligopoly games where one property holds while the other does not, so that either (i) the open-loop Nash equilibrium is subgame perfect while the stackelberg one is time inconsistent, or (ii) the open-loop Nash and Stackelberg equilibria are only weakly time consistent.

Suggested Citation

  • R. Cellini & L. Lambertini & G. Leitmann, 2004. "Perfect Uncontrollable Differential Games," Working Papers 509, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:509
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4783/1/509.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Amir, Rabah, 1996. "Cournot Oligopoly and the Theory of Supermodular Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 132-148, August.
    2. Cellini, Roberto & Lambertini, Luca, 1998. "A Dynamic Model of Differentiated Oligopoly with Capital Accumulation," Journal of Economic Theory, Elsevier, vol. 83(1), pages 145-155, November.
    3. Karp, Larry & Lee, In Ho, 2000. "Time-Consistent Policies," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt94q3m5mq, Department of Agricultural & Resource Economics, UC Berkeley.
    4. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
    5. Lucas, Robert Jr. & Stokey, Nancy L., 1983. "Optimal fiscal and monetary policy in an economy without capital," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 55-93.
    6. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-1164, September.
    7. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August.
    8. Xie, Danyang, 1997. "On Time Inconsistency: A Technical Issue in Stackelberg Differential Games," Journal of Economic Theory, Elsevier, vol. 76(2), pages 412-430, October.
    9. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
    10. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
    11. Karp, Larry, 2003. "Time-Consistent Policies," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt7br39238, Department of Agricultural & Resource Economics, UC Berkeley.
    12. R. Cellini & L. Lambertini, 2000. "Dynamic Oligopoly with Sticky Prices: Closed-Loop,Feedback and Open-Loop Solutions," Working Papers 393, Dipartimento Scienze Economiche, Universita' di Bologna.
    13. Kamien, Morton I. & Zang, Israel, 2000. "Meet me halfway: research joint ventures and absorptive capacity," International Journal of Industrial Organization, Elsevier, vol. 18(7), pages 995-1012, October.
    14. Karp, Larry & Lee, In Ho, 2003. "Time-consistent policies," Journal of Economic Theory, Elsevier, vol. 112(2), pages 353-364, October.
    15. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, April.
    16. Clemhout, S & Leitmann, G & Wan, H Y, Jr, 1971. "A Differential Game Model of Duopoly," Econometrica, Econometric Society, vol. 39(6), pages 911-938, November.
    17. Daniel Cohen & Philippe Michel, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 55(2), pages 263-274.
    18. R. Cellini & L. Lambertini, 2003. "On the Dynamic Consistency of Optimal Monetary Policy," Working Papers 463, Dipartimento Scienze Economiche, Universita' di Bologna.
    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. Cellini, Roberto & Lambertini, Luca, 2007. "Time consistent fiscal policies in a Ramsey economy," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 296-313, May.

    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. Cellini, Roberto & Lambertini, Luca, 2007. "Time consistent fiscal policies in a Ramsey economy," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 296-313, May.
    2. Roberto Cellini & Luca Lambertini, 2010. "The Issue Of Time Inconsistency Revisited As An Extended Game," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(02), pages 161-174.
    3. Lambertini, Luca & Mantovani, Andrea, 2006. "Identifying reaction functions in differential oligopoly games," Mathematical Social Sciences, Elsevier, vol. 52(3), pages 252-271, December.
    4. George E. Halkos & George J. Papageorgiou, 2012. "Pollution Control Policy: A Dynamic Taxation Scheme," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 6(1), pages 14-37, March.
    5. R. Cellini & L. Lambertini, 2003. "On the Dynamic Consistency of Optimal Monetary Policy," Working Papers 463, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Baldini, Massimo & Lambertini, Luca, 2011. "Profit taxation and capital accumulation in a dynamic oligopoly model," Japan and the World Economy, Elsevier, vol. 23(1), pages 13-18, January.
    7. Chu, Angus C., 2011. "The welfare cost of one-size-fits-all patent protection," Journal of Economic Dynamics and Control, Elsevier, vol. 35(6), pages 876-890, June.
    8. Larry Karp & Jiangfeng Zhang, 2016. "Taxes Versus Quantities for a Stock Pollutant with Endogenous Abatement Costs and Asymmetric Information," Studies in Economic Theory, in: Graciela Chichilnisky & Armon Rezai (ed.), The Economics of the Global Environment, pages 493-533, Springer.
    9. Guido Tabellini, 2005. "Finn Kydland and Edward Prescott's Contribution to the Theory of Macroeconomic Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 107(2), pages 203-216, June.
    10. Chu, Angus C., 2009. "A politico-economic analysis of the European Union's R&D policy," Journal of Macroeconomics, Elsevier, vol. 31(4), pages 582-590, December.
    11. Persson, Torsten & Tabellini, Guido, 1999. "Political economics and macroeconomic policy," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 22, pages 1397-1482, Elsevier.
    12. Ansgar Belke & Ralph Setzer, 2004. "Nobelpreis für Wirtschaftswissenschaften 2004 an Finn E. Kydland and Edward C. Prescott," Diskussionspapiere aus dem Institut für Volkswirtschaftslehre der Universität Hohenheim 248/2004, Department of Economics, University of Hohenheim, Germany.
    13. Chakraborty, Bidisha & Gupta, Manash Ranjan, 2009. "Human capital, inequality, endogenous growth and educational subsidy: A theoretical analysis," Research in Economics, Elsevier, vol. 63(2), pages 77-90, June.
    14. P Arestis & A Mihailov, 2009. "Flexible Rules cum Constrained Discretion: A New Consensus in Monetary Policy," Economic Issues Journal Articles, Economic Issues, vol. 14(2), pages 27-54, September.
    15. Alesina, Alberto & Stella, Andrea, 2010. "The Politics of Monetary Policy," Handbook of Monetary Economics, in: Benjamin M. Friedman & Michael Woodford (ed.), Handbook of Monetary Economics, edition 1, volume 3, chapter 18, pages 1001-1054, Elsevier.
    16. Dennis, Richard & Kirsanova, Tatiana, 2010. "Expectations Traps and Coordination Failures: Selecting among Multiple Discretionary Equilibria," MPRA Paper 24616, University Library of Munich, Germany.
    17. Kurozumi, Takushi, 2008. "Optimal sustainable monetary policy," Journal of Monetary Economics, Elsevier, vol. 55(7), pages 1277-1289, October.
    18. Christos Koulovatianos & Leonard J. Mirman, 2005. "Endogenous Public Policy and Long-Run Growth: Some Simple Analytics," Vienna Economics Papers 0502, University of Vienna, Department of Economics.
    19. Albanesi, Stefania, 2003. "Optimal and Time-Consistent Monetary and Fiscal Policy with Heterogeneous Agents," CEPR Discussion Papers 3713, C.E.P.R. Discussion Papers.
    20. AMIR, Rabah, 2001. "Stochastic games in economics and related fields: an overview," LIDAM Discussion Papers CORE 2001060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    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:bol:bodewp:509. 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: Dipartimento Scienze Economiche, Universita' di Bologna (email available below). General contact details of provider: https://edirc.repec.org/data/sebolit.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.