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Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames

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Author Info
Dechenaux, Emmanuel
Kovenock, Dan

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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.

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Publisher Info
Paper provided by Purdue University, Department of Economics in its series Purdue University Economics Working Papers with number 1164.

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Length: 46 pages
Date of creation: 2003
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Handle: RePEc:pur:prukra:1164

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Related research
Keywords: Bertrand-Edgeworth ; Supergame ; Collusion ; Capacity;

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Find related papers by JEL classification:
C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
D43 - Microeconomics - - Market Structure and Pricing - - - 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

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Allen, B. & Deneckere, R. & Faith, T. & Kovenock, D., 1994. "Capacity Precommitment as a Barrier to Entry: A Bertrand-Edgeworth Approach," Purdue University Economics Working Papers 1062, Purdue University, Department of Economics.
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  2. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Blackwell Publishing, vol. 51(3), pages 271-293, 09. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March. [Downloadable!] (restricted)
  5. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June. [Downloadable!] (restricted)
  6. 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. [Downloadable!] (restricted)
  7. 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. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  9. Judith R. Gelman & Steven C. Salop, 1983. "Judo Economics: Capacity Limitation and Coupon Competition," Bell Journal of Economics, The RAND Corporation, vol. 14(2), pages 315-325, Autumn. [Downloadable!] (restricted)
  10. Brock, William A & Scheinkman, Jose A, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Blackwell Publishing, vol. 52(3), pages 371-82, July. [Downloadable!] (restricted)
  11. 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 521-41, August. [Downloadable!] (restricted)
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  12. 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 301-09, March. [Downloadable!] (restricted)
  13. Davidson, Carl & Deneckere, Raymond, 1984. "Horizontal mergers and collusive behavior," International Journal of Industrial Organization, Elsevier, vol. 2(2), pages 117-132, June. [Downloadable!] (restricted)
  14. Allen, Franklin & Faulhaber, Gerald R, 1991. "Rational Rationing," Economica, London School of Economics and Political Science, vol. 58(230), pages 189-98, May. [Downloadable!] (restricted)
  15. Boyer, Marcel & Moreaux, Michel, 1988. "Rational Rationing in Stackelberg Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 103(2), pages 409-14, May. [Downloadable!] (restricted)
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  16. Benoit, Jean-Pierre & Krishna, Vijay, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Blackwell Publishing, vol. 54(1), pages 23-35, January. [Downloadable!] (restricted)
  17. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January. [Downloadable!] (restricted)
  18. Rees, Ray, 1993. "Collusive Equilibrium in the Great Salt Duopoly," Economic Journal, Royal Economic Society, vol. 103(419), pages 833-48, July. [Downloadable!] (restricted)
  19. 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 877-88, November. [Downloadable!] (restricted)
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  20. Lambson, Val Eugene, 1987. "Optimal Penal Codes in Price-Setting Supergames with Capacity Constraints," Review of Economic Studies, Blackwell Publishing, vol. 54(3), pages 385-97, July. [Downloadable!] (restricted)
  21. 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. [Downloadable!] (restricted)
  22. Richard J. Gilbert & Paul Klemperer, 2000. "An Equilibrium Theory of Rationing," RAND Journal of Economics, The RAND Corporation, vol. 31(1), pages 1-21, Spring.
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dechenaux, Emmanuel & Kovenock, Dan, 2005. "Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions," Working Paper Series 636, Research Institute of Industrial Economics. [Downloadable!]
    Other versions:
  2. 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). [Downloadable!]
  3. de Frutos, Maria-Angeles & Fabra, Natalia, 2007. "Endogenous Capacities and Price Competition: The Role of Demand Uncertainty," CEPR Discussion Papers 6096, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  4. Puzzello, Daniela, 2006. "Tie-Breaking Rules and Divisibility in Experimental Duopoly Markets," MPRA Paper 6453, University Library of Munich, Germany. [Downloadable!]
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