IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v47y2011i1p29-74.html
   My bibliography  Save this article

Endogenous rationing, price dispersion and collusion in capacity constrained supergames

Author

Listed:
  • Emmanuel Dechenaux

    ()

  • Dan Kovenock

Abstract

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For a wide range of capacity pairs, the equilibrium path providing the smaller firm with its highest stationary perfect equilibrium payoff requires that it undercut its rival’s price and ration demand. Furthermore, for some capacities and discount factors supporting security level punishments, price shading and rationing arise everywhere on the set of stationary perfect equilibrium paths yielding (constrained) Pareto optimal payoffs. That is, price shading may not only be consistent with successful collusion, it may be a requirement of successful collusion.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
  • Handle: RePEc:spr:joecth:v:47:y:2011:i:1:p:29-74
    DOI: 10.1007/s00199-010-0527-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00199-010-0527-0
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006. "Designing electricity auctions," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 23-46, March.
    2. Val Eugene Lambson, 1987. "Optimal Penal Codes in Price-setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 54(3), pages 385-397.
    3. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, vol. 15(3), pages 349-368, May.
    4. Lambson Val Eugene, 1994. "Some Results on Optimal Penal Codes in Asymmetric Bertrand Supergames," Journal of Economic Theory, Elsevier, vol. 62(2), pages 444-468, April.
    5. Jean-Pierre Benoit & Vijay Krishna, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 23-35.
    6. Lambson, Val Eugene, 1995. "Optimal penal codes in nearly symmetric Bertrand supergames with capacity constraints," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 1-22.
    7. Davidson, Carl & Deneckere, Raymond J, 1990. "Excess Capacity and Collusion," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 521-541, August.
    8. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    9. Osborne, Martin J & Pitchik, Carolyn, 1987. "Cartels, Profits and Excess Capacity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 413-428, June.
    10. Albaek, Svend & Mollgaard, Peter & Overgaard, Per B, 1997. "Government-Assisted Oligopoly Coordination? A Concrete Case," Journal of Industrial Economics, Wiley Blackwell, vol. 45(4), pages 429-443, December.
    11. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    12. Emmanuel Dechenaux & Dan Kovenock, 2007. "Tacit collusion and capacity withholding in repeated uniform price auctions," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1044-1069, December.
    13. Dixon, Huw David, 1992. "The Competitive Outcome as the Equilibrium in an Edgeworthian Price-Quantity Model," Economic Journal, Royal Economic Society, vol. 102(411), pages 301-309, March.
    14. Allen, Franklin & Faulhaber, Gerald R, 1991. "Rational Rationing," Economica, London School of Economics and Political Science, vol. 58(230), pages 189-198, May.
    15. Rees, Ray, 1993. "Collusive Equilibrium in the Great Salt Duopoly," Economic Journal, Royal Economic Society, vol. 103(419), pages 833-848, July.
    16. Boyer, Marcel & Moreaux, Michel, 1989. "Endogenous Rationing in a Differentiated Product Duopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 877-888, November.
    17. Val Eugene Lambson & J. David Richardson, 1992. "Empirical Evidence for Collusion in the U.S. Auto Market?," NBER Working Papers 4111, National Bureau of Economic Research, Inc.
    18. 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.
    19. Marcel Boyer & Michel Moreaux, 1988. "Rational Rationing in Stackelberg Equilibria," The Quarterly Journal of Economics, Oxford University Press, vol. 103(2), pages 409-414.
    20. Rees, Ray, 1993. "Collusive Equilibrium in the Great Salt Duopoly," Munich Reprints in Economics 3413, University of Munich, Department of Economics.
    21. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 271-293, September.
    22. Benoit, Jean-Pierre & Krishna, Vijay, 1991. "Entry deterrence and dynamic competition : The role of capacity reconsidered," International Journal of Industrial Organization, Elsevier, vol. 9(4), pages 477-495, December.
    23. Sorgard, Lars, 1997. "Erratum to "Judo economics reconsidered: Capacity limitation, entry and collusion" [International journal of industrial organization 15 (1997) 349-368]," International Journal of Industrial Organization, Elsevier, vol. 15(5), pages 635-635, August.
    24. Davidson, Carl & Deneckere, Raymond, 1984. "Horizontal mergers and collusive behavior," International Journal of Industrial Organization, Elsevier, vol. 2(2), pages 117-132, June.
    25. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
    26. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Oxford University Press, vol. 52(3), pages 371-382.
    27. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
    28. 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.
    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. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 29-74, May.
    2. Daniel Cracau & Benjamin Franz, 2012. "An experimental study of mixed strategy equilibria in simultaneous price-quantity games," FEMM Working Papers 120017, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    3. Zoltán Rácz & Attila Tasnádi, 2016. "A Bertrand–Edgeworth oligopoly with a public firm," Journal of Economics, Springer, vol. 119(3), pages 253-266, November.
    4. 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.
    5. SANIN, Maria Eugenia, 2006. "Market design in wholesale electricity markets," CORE Discussion Papers 2006100, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. de Frutos, María-Ángeles & Fabra, Natalia, 2011. "Endogenous capacities and price competition: The role of demand uncertainty," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 399-411, July.
    7. Emmanuel Dechenaux & Dan Kovenock, 2007. "Tacit collusion and capacity withholding in repeated uniform price auctions," RAND Journal of Economics, RAND Corporation, vol. 38(4), pages 1044-1069, December.
    8. Knittel, Christopher R. & Lepore, Jason J., 2010. "Tacit collusion in the presence of cyclical demand and endogenous capacity levels," International Journal of Industrial Organization, Elsevier, vol. 28(2), pages 131-144, March.
    9. Puzzello, Daniela, 2008. "Tie-breaking rules and divisibility in experimental duopoly markets," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 164-179, July.
    10. Liu, Xuyuan & Lu, Jingfeng, 2017. "Optimal prize-rationing strategy in all-pay contests with incomplete information," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 57-90.

    More about this item

    Keywords

    Bertrand–Edgeworth; Supergame; Collusion; Capacity; C73; D43; L13; L41;

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L41 - Industrial Organization - - Antitrust Issues and Policies - - - Monopolization; Horizontal Anticompetitive Practices

    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:spr:joecth:v:47:y:2011:i:1:p:29-74. 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: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: http://www.springer.com .

    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.