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Perfect Uncontrollable Differential Games

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

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.

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Paper provided by Dipartimento Scienze Economiche, Universita' di Bologna in its series Working Papers with number 509.

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Date of creation: 2004
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Handle: RePEc:bol:bodewp:509
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  1. 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.
  2. 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.
  3. 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.
  4. R. Cellini & L. Lambertini, 2003. "On the Dynamic Consistency of Optimal Monetary Policy," Working Papers 463, Dipartimento Scienze Economiche, Universita' di Bologna.
  5. Clemhout, S & Leitmann, G & Wan, H Y, Jr, 1971. "A Differential Game Model of Duopoly," Econometrica, Econometric Society, vol. 39(6), pages 911-38, November.
  6. 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.
  7. 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 473-91, June.
  8. 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.
  9. 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.
  10. Danyang Xie, 2002. "On Time Inconsistency: A Technical Issue in Stackelberg Differential Games," Macroeconomics 0212004, EconWPA.
  11. 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.
  12. AMIR, Rabah, 1994. "Cournot Oligopoly and the Theory of Supermodular Games," CORE Discussion Papers 1994013, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Fershtman, Chaim & Kamien, Morton I, 1987. "Dynamic Duopolistic Competition with Sticky Prices," Econometrica, Econometric Society, vol. 55(5), pages 1151-64, September.
  14. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  15. 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.
  16. Daniel Cohen & Philippe Michel, 1988. "How Should Control Theory Be Used to Calculate a Time-Consistent Government Policy?," Review of Economic Studies, Oxford University Press, vol. 55(2), pages 263-274.
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