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 Paris 1 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.science/hal-00709093v2
    as

    Download full text from publisher

    File URL: https://hal.science/hal-00709093v2/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384, December.
    2. 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.
    3. 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.
    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. 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.
    8. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    15. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
    16. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    17. 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.
    18. Roy Chowdhury, Prabal, 2009. "Bertrand competition with non-rigid capacity constraints," Economics Letters, Elsevier, vol. 103(1), pages 55-58, April.
    19. Dastidar, Krishnendu Ghosh, 2011. "Bertrand equilibrium with subadditive costs," Economics Letters, Elsevier, vol. 112(2), pages 202-204, August.
    20. 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.
    21. James W. Friedman, 1973. "A Non-cooperative Equilibrium for Supergames: A Correction," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 40(3), pages 435-435.
    22. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    23. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(1), pages 23-35.
    24. 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.
    25. Switgard Feuerstein, 2005. "Collusion in Industrial Economics—A Survey," Journal of Industry, Competition and Trade, Springer, vol. 5(3), pages 163-198, December.
    26. 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.
    27. David M. Kreps & Jose A. Scheinkman, 1983. "Quantity Precommitment and Bertrand Competition Yield Cournot Outcomes," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 326-337, Autumn.
    28. Prabal Roy Chowdhury, 2009. "Bertrand competition with non-rigid capacity constraints," Discussion Papers 09-02, Indian Statistical Institute, Delhi.
    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, 2024. "Bertrand competition in vertically related markets," Applied Economics Letters, Taylor & Francis Journals, vol. 31(6), pages 524-529, March.
    4. Werner Güth & Manfred Stadler & Alexandra Zaby, 2019. "Coordination Failure in Capacity-then-Price-Setting Games," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 36(3), pages 111-133, December.
    5. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    6. Elpiniki Bakaouka & Marc Escrihuela-Villar & Walter Ferrarese, 2022. "Endogenous Horizontal Mergers in Homogeneous Goods Industries with Bertrand Competition," DEA Working Papers 96, Universitat de les Illes Balears, Departament d'Economía Aplicada.
    7. Kazuhiro Takauchi & Tomomichi Mizuno, 2022. "Endogenous transport price, R&D spillovers, and trade," The World Economy, Wiley Blackwell, vol. 45(5), pages 1477-1500, May.
    8. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Working Papers halshs-01174291, HAL.
    9. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2021. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Working Papers halshs-03378500, HAL.
    10. Kazuhiro Takauchi & Tomomichi Mizuno, 2019. "Is competition in the transport industry bad?A welfare analysis of R&D with inter-regional transportation," Discussion Papers 1910, Graduate School of Economics, Kobe University.
    11. Tomomichi Mizuno & Kazuhiro Takauchi, 2020. "Optimal Export Policy With Upstream Price Competition," Manchester School, University of Manchester, vol. 88(2), pages 324-348, March.
    12. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2022. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Post-Print halshs-03378500, HAL.
    13. WAUTHY, Xavier Y., 2014. "From Bertrand to Cournot via Kreps and Scheinkman: a hazardous journey," LIDAM Discussion Papers CORE 2014026, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "Soft-Capacity constrained price competition with entry and a minimum firm size: Chamberlin without differentiation," Working Papers hal-02909801, HAL.
    15. Marie‐Laure Cabon‐Dhersin & Nicolas Drouhin, 2023. "Chamberlin without differentiation: Soft capacity constrained price competition with free entry," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 118-126, March.
    16. Burguet, Roberto & Sákovics, József, 2014. "Bertrand and the long run," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-38, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2020. "A general model of price competition with soft capacity constraints," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(1), pages 95-120, July.
    2. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2010. "The end of the Bertrand Paradox?," Post-Print halshs-00542486, HAL.
    3. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Post-Print hal-02356872, HAL.
    4. 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.
    5. Makoto Yano & Takashi Komatsubara, 2018. "Price competition or price leadership," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(4), pages 1023-1057, December.
    6. Makoto Yano & Takashi Komatsubara, 2012. "Price Competition or Tacit Collusion," KIER Working Papers 807, Kyoto University, Institute of Economic Research.
    7. 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.
    8. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2021. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Working Papers halshs-03378500, HAL.
    9. Alejandro Saporiti & German Coloma, 2008. "Bertrand's price competition in markets with fixed costs," RCER Working Papers 541, University of Rochester - Center for Economic Research (RCER).
    10. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2022. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Post-Print halshs-03378500, HAL.
    11. R. R. Routledge & R. A. Edwards, 2020. "Ambiguity and price competition," Theory and Decision, Springer, vol. 88(2), pages 231-256, March.
    12. Matsumura, Toshihiro, 2012. "Welfare consequence of an asymmetric regulation in a mixed Bertrand duopoly," Economics Letters, Elsevier, vol. 115(1), pages 94-96.
    13. António Brandão & Joana Pinho & Hélder Vasconcelos, 2014. "Asymmetric Collusion with Growing Demand," Journal of Industry, Competition and Trade, Springer, vol. 14(4), pages 429-472, December.
    14. Marie‐Laure Cabon‐Dhersin & Nicolas Drouhin, 2023. "Chamberlin without differentiation: Soft capacity constrained price competition with free entry," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(1), pages 118-126, March.
    15. R. A. Edwards & R. R. Routledge, 2023. "Existence and uniqueness of Nash equilibrium in discontinuous Bertrand games: a complete characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(2), pages 569-586, June.
    16. 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.
    17. Blavatskyy, Pavlo, 2018. "Oligopolistic price competition with a continuous demand," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 123-131.
    18. Trost, Michael, 2022. "Unraveling the spreading pattern of collusively effective competition clauses," Hohenheim Discussion Papers in Business, Economics and Social Sciences 01-2022, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    19. Lambertini, Luca, 1997. "Prisoners' Dilemma in Duopoly (Super)Games," Journal of Economic Theory, Elsevier, vol. 77(1), pages 181-191, November.
    20. R. R. Routledge, 2013. "On the existence of coalition-proof Bertrand equilibrium," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 21-31, May.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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.

    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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.