IDEAS home Printed from https://ideas.repec.org/p/bol/bodewp/wp1043.html
   My bibliography  Save this paper

Parabolic Cylinders and Folk Theorems

Author

Listed:
  • F. Delbono
  • L. Lambertini

Abstract

We study a class of games featuring payoff functions being parabolic cylinders where best reply functions are orthogonal and therefore the pure-strategy non-cooperative solution is attained as a Nash equilibrium in dominant strategies. We prove that the resulting threshold of the discount factor above which implicit collusion on the Pareto frontier is stable in the infi?nite supergames is independent of the number of players. This holds irrespective of whether punishment is based on in?finite Nash reversion or one-shot stick-and-carrot strategy. We outline two examples stemming from economic theory and one from international relations.

Suggested Citation

  • F. Delbono & L. Lambertini, 2015. "Parabolic Cylinders and Folk Theorems," Working Papers wp1043, Dipartimento Scienze Economiche, Universita' di Bologna.
    • Handle: RePEc:bol:bodewp:wp1043
    as

    Download full text from publisher

    File URL: http://amsacta.unibo.it/4415/1/WP1043.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(1), pages 1-12.
    2. Luca Lambertini & Dan Sasaki, 2002. "Non‐Negative Quantity Constraints and the Duration of Punishment," The Japanese Economic Review, Japanese Economic Association, vol. 53(1), pages 77-93, March.
    3. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, April.
    4. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, April.
    5. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    Full references (including those not matched with items on IDEAS)

    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. F. Delbono & L. Lambertini, 2016. "On Globally Optimal Punishments in the Repeated Cournot Game," Working Papers wp1091, Dipartimento Scienze Economiche, Universita' di Bologna.
    2. Belleflamme,Paul & Peitz,Martin, 2015. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9781107687899.
    3. Garrod, Luke, 2012. "Collusive price rigidity under price-matching punishments," International Journal of Industrial Organization, Elsevier, vol. 30(5), pages 471-482.
    4. Etienne Billette de Villemeur & Laurent Flochel & Bruno Versaevel, 2013. "Optimal collusion with limited liability," International Journal of Economic Theory, The International Society for Economic Theory, vol. 9(3), pages 203-227, September.
    5. Kaplow, Louis & Shapiro, Carl, 2007. "Antitrust," Handbook of Law and Economics, in: A. Mitchell Polinsky & Steven Shavell (ed.), Handbook of Law and Economics, edition 1, volume 2, chapter 15, pages 1073-1225, Elsevier.
    6. Pierre-Pascal Gendron, 1996. "Corporation Tax Asymmetries: An Oligopolistic Supergame Analysis," Working Papers ecpap-96-04, University of Toronto, Department of Economics.
    7. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    8. Lambertini, Luca & Marattin, Luigi, 2021. "On prices’ cyclical behaviour in oligopolistic markets," Research in Economics, Elsevier, vol. 75(1), pages 79-86.
    9. Baldelli, Serena & Lambertini, Luca, 2006. "Price vs quantity in a duopoly supergame with Nash punishments," Research in Economics, Elsevier, vol. 60(3), pages 121-130, September.
    10. Stefano Colombo, 2009. "The unidirectional Hotelling model with spatial price discrimination," Economics Bulletin, AccessEcon, vol. 29(4), pages 3031-3040.
    11. Hélder Vasconcelos, 2008. "Sustaining Collusion in Growing Markets," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 17(4), pages 973-1010, December.
    12. Lu, Yuanzhu & Wright, Julian, 2010. "Tacit collusion with price-matching punishments," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 298-306, May.
    13. Robert Gagné & Simon van Norden & Bruno Versaevel, 2003. "Testing Optimal Punishment Mechanisms Under Price Regulation: the Case of the Retail Market for Gasoline," CIRANO Working Papers 2003s-57, CIRANO.
    14. repec:lic:licosd:43022 is not listed on IDEAS
    15. Colombo, Luca & Labrecciosa, Paola, 2006. "Optimal punishments with detection lags," Economics Letters, Elsevier, vol. 92(2), pages 198-201, August.
    16. Agisilaou, Panayiotis, 2012. "Keep to sustain or keep to exploit? Why firms keep hard evidence," MPRA Paper 39109, University Library of Munich, Germany.
    17. Kessing, Sebastian G. & Konrad, Kai A. & Kotsogiannis, Christos, 2006. "Federal tax autonomy and the limits of cooperation," Journal of Urban Economics, Elsevier, vol. 59(2), pages 317-329, March.
    18. Ivaldi, Marc & Jullien, Bruno & Rey, Patrick & Seabright, Paul & Tirole, Jean, 2003. "The Economics of Tacit Collusion," IDEI Working Papers 186, Institut d'Économie Industrielle (IDEI), Toulouse.
    19. Agisilaou, Panayiotis, 2011. "Keep to sustain or keep to exploit? Why firms keep hard evidence," MPRA Paper 30963, University Library of Munich, Germany.
    20. Switgard Feuerstein, 2005. "Collusion in Industrial Economics—A Survey," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 163-198, December.
    21. Svensson, J, 1996. "Collusion Among Interest Groups : Foreign Aid and Rent-Dissipation," Papers 610, Stockholm - International Economic Studies.

    More about this item

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    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:wp1043. 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.