IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/hal-00709093.html
   My bibliography  Save this paper

Tacit collusion in a one-shot game of price competition with soft capacity constraints

Author

Listed:
  • Marie-Laure Cabon-Dhersin

    () (CREAM - Centre de Recherche en Economie Appliquée à la Mondialisation - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université - IRIHS - Institut de Recherche Interdisciplinaire Homme et Société - UNIROUEN - Université de Rouen Normandie - NU - Normandie Université)

  • Nicolas Drouhin

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper analyses price competition in the case of two firms operating under constant returns to scale with more than one production factor. Factors are chosen sequentially in a two-stage game generating a soft capacity constraint and implying a convex short term cost function in the second stage of the game. We show that tacit collusion is the only predictable result of the whole game i.e. the unique payoff-dominant pure strategy Nash equilibrium. Technically, this paper bridges the capacity constraint literature on price competition and that of the convex cost function.

Suggested Citation

  • Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2012. "Tacit collusion in a one-shot game of price competition with soft capacity constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00709093, HAL.
    • Handle: RePEc:hal:cesptp:hal-00709093
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00709093v2
    as

    Download full text from publisher

    File URL: https://hal.archives-ouvertes.fr/hal-00709093v2/document
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dastidar, Krishnendu Ghosh, 1995. "On the Existence of Pure Strategy Bertrand Equilibrium," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 19-32, January.
    2. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 23-35.
    3. James W. Friedman, 1971. "A Non-cooperative Equilibrium for Supergames," Review of Economic Studies, Oxford University Press, vol. 38(1), pages 1-12.
    4. Cooper, Russell, et al, 1990. "Selection Criteria in Coordination Games: Some Experimental Results," American Economic Review, American Economic Association, vol. 80(1), pages 218-233, March.
    5. Steffen Hoernig, 2007. "Bertrand Games and Sharing Rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(3), pages 573-585, June.
    6. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2010. "The end of the Bertrand Paradox ?," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00542486, HAL.
    7. Abbink, Klaus & Brandts, Jordi, 2008. "24. Pricing in Bertrand competition with increasing marginal costs," Games and Economic Behavior, Elsevier, vol. 63(1), pages 1-31, May.
    8. Roy Chowdhury, Prabal, 2009. "Bertrand competition with non-rigid capacity constraints," Economics Letters, Elsevier, vol. 103(1), pages 55-58, April.
    9. Tom Ross & Russell Cooper & Douglas V. DeJong & Robert Forsythe, 1987. "Selection Criteria in Coordination Games: Some Experimental Results," Carleton Industrial Organization Research Unit (CIORU) 87-04, Carleton University, Department of Economics.
    10. Dan Kovenock & Raymond Deneckere & Tom Faith & Beth Allen, 2000. "Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 15(3), pages 501-530.
    11. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    12. Krishnendu Ghosh Dastidar, 2011. "Existence of Bertrand equilibrium revisited," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(4), pages 331-350, December.
    13. Hoernig, Steffen H., 2002. "Mixed Bertrand equilibria under decreasing returns to scale: an embarrassment of riches," Economics Letters, Elsevier, vol. 74(3), pages 359-362, February.
    14. Novshek, William & Chowdhury, Prabal Roy, 2003. "Bertrand equilibria with entry: limit results," International Journal of Industrial Organization, Elsevier, vol. 21(6), pages 795-808, June.
    15. Switgard Feuerstein, 2005. "Collusion in Industrial Economics—A Survey," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 163-198, December.
    16. Bagh, Adib, 2010. "Pure strategy equilibria in Bertrand games with discontinuous demand and asymmetric tie-breaking rules," Economics Letters, Elsevier, vol. 108(3), pages 277-279, September.
    17. Dixon, Huw, 1986. "The Cournot and Bertrand Outcomes as Equilibria in a Strategic Metagame," Economic Journal, Royal Economic Society, vol. 96(380a), pages 59-70, Supplemen.
    18. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
    19. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    20. Saporiti Alejandro & Coloma Germán, 2010. "Bertrand Competition in Markets with Fixed Costs," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-30, June.
    21. Dastidar, Krishnendu Ghosh, 2011. "Bertrand equilibrium with subadditive costs," Economics Letters, Elsevier, vol. 112(2), pages 202-204, August.
    22. Todd R. Kaplan & David Wettstein, 2000. "The possibility of mixed-strategy equilibria with constant-returns-to-scale technology under Bertrand competition," Spanish Economic Review, Springer;Spanish Economic Association, vol. 2(1), pages 65-71.
    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. Burguet, Roberto & Sákovics, József, 2017. "Bertrand and the long run," International Journal of Industrial Organization, Elsevier, vol. 51(C), pages 39-55.
    2. Cabon-Dhersin Marie-Laure & Drouhin Nicolas, 2017. "A general model of price competition with soft capacity constraints," Working Papers 2017-56, Center for Research in Economics and Statistics.
    3. Tomomichi Mizuno & Kazuhiro Takauchi, 2018. "Optimal export policy with upstream price competition," Discussion Papers 1805, Graduate School of Economics, Kobe University.
    4. WAUTHY, Xavier Y., 2014. "From Bertrand to Cournot via Kreps and Scheinkman: a hazardous journey," CORE Discussion Papers 2014026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Working Papers halshs-01174291, HAL.

    More about this item

    Keywords

    price competition; tacit collusion; convex cost; Bertrand Paradox; capacity constraint;

    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:hal:cesptp:hal-00709093. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.