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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, ENS Cachan - École normale supérieure - Cachan)

Abstract

This paper analyzes 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, that is, 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, 2014. "Tacit Collusion in a One-Shot Game of Price Competition with Soft Capacity Constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01311142, HAL.
    • Handle: RePEc:hal:cesptp:hal-01311142
    DOI: 10.1111/jems.12049
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    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. Kazuhiro Takauchi & Tomomichi Mizuno & Qing Hu, 2025. "Rules of origin and regional upstream competition," Discussion Papers 2519, Graduate School of Economics, Kobe University.
    3. 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.
    4. Tomomichi Mizuno & Kazuhiro Takauchi, 2024. "Bertrand competition in vertically related markets," Applied Economics Letters, Taylor & Francis Journals, vol. 31(6), pages 524-529, March.
    5. 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.
    6. 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.
    7. 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.
    8. Gian Luigi Albano & Walter Ferrarese & Roberto Pezzuto, 2025. "When Fewer Bids Increase Competition: Buyer Surplus Enhancing Mergers in Single-Award Procurement Auctions," CEIS Research Paper 607, Tor Vergata University, CEIS, revised 09 Jul 2025.
    9. 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.
    10. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2021. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Working Papers halshs-03378500, HAL.
    11. 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.
    12. Tomomichi Mizuno & Kazuhiro Takauchi, 2020. "Optimal Export Policy With Upstream Price Competition," Manchester School, University of Manchester, vol. 88(2), pages 324-348, March.
    13. Marie-Laure Cabon-Dhersin & Nicolas Drouhin, 2022. "Chamberlin without differentiation: Soft-capacity constrained price competition with free entry," Post-Print halshs-03378500, HAL.
    14. 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).
    15. 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.
    16. Marie-Laure Cabon-Dhersin & Jonas Didisse, 2017. "Inter-university competition and high tuition fees," Post-Print hal-02356872, HAL.
    17. 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.
    18. 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).

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