IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/535.html
   My bibliography  Save this paper

Degenerate Feedback and Time Consistency in Dynamic 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' 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
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4755/1/535.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. R. Cellini & L. Lambertini, 2003. "Advertising in a Differential Oligopoly Game," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 61-81, January.
    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. 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.
    5. Spence, Michael, 1976. "Product Differentiation and Welfare," American Economic Review, American Economic Association, vol. 66(2), pages 407-414, May.
    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. 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.
    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. L. Lambertini, 2005. "Dynamic Oligopoly 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. 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).
    4. 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.
    5. L. Lambertini & A. Palestini & A. Tampieri, 2014. "CSR in an Asymmetric Duopoly with Environmental Externalities," Working Papers wp959, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Dragone, Davide & Lambertini, Luca & Palestini, Arsen, 2022. "Emission taxation, green innovations and inverted-U aggregate R&D efforts in a linear state differential game," Research in Economics, Elsevier, vol. 76(1), pages 62-68.
    7. R. Cellini & L. Lambertini, 2008. "Weak and Strong Time Consistency in a Differential Oligopoly Game with Capital Accumulation," Journal of Optimization Theory and Applications, Springer, vol. 138(1), pages 17-26, July.
    8. 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.

    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. Luca Lambertini & Andrea Mantovani, 2010. "Process and product innovation: A differential game approach to product life cycle," International Journal of Economic Theory, The International Society for Economic Theory, vol. 6(2), pages 227-252, June.
    2. Cellini, Roberto & Lambertini, Luca, 2007. "A differential oligopoly game with differentiated goods and sticky prices," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1131-1144, January.
    3. R. Cellini & L. Lambertini, 2000. "Differential Games and Oligopoly Theory: An Overview," Working Papers 369, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. R. Cellini & L. Lambertini, 2002. "Advertising with Spillover Effects in a Differential Oligopoly Game With Differentiated Goods," Working Papers 430, Dipartimento Scienze Economiche, Universita' di Bologna.
    5. R. Cellini & L. Lambertini & G. Leitmann, 2004. "Perfect Uncontrollable Differential Games," Working Papers 509, Dipartimento Scienze Economiche, Universita' di Bologna.
    6. Lambertini, Luca & Mantovani, Andrea, 2009. "Process and product innovation by a multiproduct monopolist: A dynamic approach," International Journal of Industrial Organization, Elsevier, vol. 27(4), pages 508-518, July.
    7. Guido Candela & Roberto Cellini, 2006. "Investment in Tourism Market: A Dynamic Model of Differentiated Oligopoly," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 35(1), pages 41-58, September.
    8. Angus Chu, 2010. "Nation states vs. united empire: Effects of political competition on economic growth," Public Choice, Springer, vol. 145(1), pages 181-195, October.
    9. R. Cellini & L. Lambertini & I. P. Ottaviano, 1999. "Growth in a Differentiated Oligopoly with Product Innovation," Working Papers 363, Dipartimento Scienze Economiche, Universita' di Bologna.
    10. Dongdong Li, 2022. "Dynamic optimal control of firms' green innovation investment and pricing strategies with environmental awareness and emission tax," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(4), pages 920-932, June.
    11. Luca Lambertini, 2009. "Optimal Product Proliferation in Monopoly: A Dynamic Analysis," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 1(1), pages 80-97, September.
    12. 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.
    13. Emanuele Bacchiega & Olivier Bonroy & Emmanuel Petrakis, 2018. "Contract contingency in vertically related markets," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 27(4), pages 772-791, October.
    14. Yingjue Zhou & Tieming Liu & Gangshu Cai, 2019. "Impact of In-Store Promotion and Spillover Effect on Private Label Introduction," Service Science, INFORMS, vol. 11(2), pages 96-112, June.
    15. Roberto Cellini & Luca Lambertini, 2011. "R&D Incentives Under Bertrand Competition: A Differential Game," The Japanese Economic Review, Japanese Economic Association, vol. 62(3), pages 387-400, September.
    16. Lambertini, Luca & Marattin, Luigi, 2021. "On prices’ cyclical behaviour in oligopolistic markets," Research in Economics, Elsevier, vol. 75(1), pages 79-86.
    17. Margarida Catalão-Lopes, 2002. "Merge or Concentrate? Some Insights for Antitrust Policy," Working Papers w200207, Banco de Portugal, Economics and Research Department.
    18. G. F. Gori & L. Lambertini, 2014. "Trade, externalities, and the impact of asymmetric information on trade policy," Working Papers wp930, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. Malcolm Brady, 2022. "Asymmetric Horizontal Differentiation under Advertising in a Cournot Duopoly," Games, MDPI, vol. 13(3), pages 1-14, May.
    20. Zanchettin, Piercarlo & Mukherjee, Arijit, 2017. "Vertical integration and product differentiation," International Journal of Industrial Organization, Elsevier, vol. 55(C), pages 25-57.

    More about this item

    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:bol:bodewp:535. 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.