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Degenerate Feedback and Time Consistency in Dynamic Games

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  • 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' and provide two examples based on (i) a model where firms invest so as to increase consumers' reservation prices, based upon Cellini and Lambertini (CEJOR, 2003); and (ii) a model where firms compete to increase their respective market shares, based upon Leitmann and Schmitendorf (IEEE Transactions on Automatic Control, 1978).

Suggested Citation

  • R. Cellini & L. Lambertini & G. Leitmann, 2005. "Degenerate Feedback and Time Consistency in Dynamic Games," Working Papers 535, Dipartimento Scienze Economiche, Universita' di Bologna.
  • Handle: RePEc:bol:bodewp:535
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    References listed on IDEAS

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    1. Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-414, May.
    2. 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.
    3. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    4. 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.
    5. 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.
    6. Cellini, Roberto & Lambertini, Luca, 2002. "A differential game approach to investment in product differentiation," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 51-62, November.
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    Cited by:

    1. L. Lambertini, 2005. "Dynamic Oligopoly ˆ la Stackelberg with Stochastic Capital Accumulation," Working Papers 547, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. repec:rim:rimwps:48-07 is not listed on IDEAS
    3. R. Cellini & L. Lambertini, 2005. "Weak and Strong Time Consistency in Differential Oligopoly Games with Capital Accumulation," Working Papers 544, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. Luca Lambertini & Arsen Palestini & Alessandro Tampieri, 2014. "CSR in an Asymmetric Duopoly with Environmental Externalities," CREA Discussion Paper Series 14-19, Center for Research in Economic Analysis, University of Luxembourg.
    5. Lambertini, Luca & Zaccour, Georges, 2015. "Inverted-U aggregate investment curves in a dynamic game of advertising," Economics Letters, Elsevier, vol. 132(C), pages 34-38.
    6. Alessandra Buratto & Luca Grosset & Bruno Viscolani, 2012. "ε-Subgame Perfectness of an Open-Loop Stackelberg Equilibrium in Linear-State Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 269-279, September.

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