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

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Listed author(s):
  • Marie-Laure Cabon-Dhersin

    ()

    (CREAM - Centre de Recherche en Economie Appliquée à la Mondialisation - Université de Rouen)

  • 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.

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File URL: https://hal.archives-ouvertes.fr/hal-00709093v2/document
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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00709093.

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Date of creation: 12 Jun 2012
Handle: RePEc:hal:cesptp:hal-00709093
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00709093v2
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Keywords: price competition; tacit collusion; convex cost; Bertrand Paradox; capacity constraint;

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  1. 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.
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  5. 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.
  6. 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.
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  8. 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.
  9. Krishnendu Dastidar, 2001. "Collusive outcomes in price competition," Journal of Economics, Springer, vol. 73(1), pages 81-93, February.
  10. 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.
  11. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  12. 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.
  13. Roy Chowdhury, Prabal, 2009. "Bertrand competition with non-rigid capacity constraints," Economics Letters, Elsevier, vol. 103(1), pages 55-58, April.
  14. Baye, Michael R. & Morgan, John, 1999. "A folk theorem for one-shot Bertrand games," Economics Letters, Elsevier, vol. 65(1), pages 59-65, October.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. Dastidar, Krishnendu Ghosh, 2011. "Bertrand equilibrium with subadditive costs," Economics Letters, Elsevier, vol. 112(2), pages 202-204, August.
  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. 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.
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Cited by:

  1. Roberto Burguet & Jozsef Sakovics, 2014. "Bertrand and the long run," ESE Discussion Papers 244, Edinburgh School of Economics, University of Edinburgh.
  2. Burguet, Roberto & Sákovics, József, 2017. "Bertrand and the long run," International Journal of Industrial Organization, Elsevier, vol. 51(C), pages 39-55.
  3. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2016. "Two University Competition Systems; Their Impact on Capacity, Tuition Fees and Admission," Working Papers halshs-01174291, HAL.
  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).

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