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

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  • Dechenaux, Emmanuel
  • Kovenock, Dan

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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Bibliographic 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
Date of revision:
Handle: RePEc:pur:prukra:1164

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

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References

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  1. 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.
  2. Dechenaux, Emmanuel & Kovenock, Dan, 2003. "Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames," Purdue University Economics Working Papers 1164, Purdue University, Department of Economics.
  3. Boyer, Marcel & Moreaux, Michel, 1988. "Rational Rationing in Stackelberg Equilibria," The Quarterly Journal of Economics, MIT Press, vol. 103(2), pages 409-14, May.
  4. 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.
  5. Davidson, Carl & Deneckere, Raymond, 1984. "Horizontal mergers and collusive behavior," International Journal of Industrial Organization, Elsevier, vol. 2(2), pages 117-132, June.
  6. Lambson, Val Eugene, 1987. "Optimal Penal Codes in Price-Setting Supergames with Capacity Constraints," Review of Economic Studies, Wiley Blackwell, vol. 54(3), pages 385-97, July.
  7. 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.
  8. Benoit, Jean-Pierre & Krishna, Vijay, 1987. "Dynamic Duopoly: Prices and Quantities," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 23-35, January.
  9. 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.
  10. Sorgard, Lars, 1997. "Judo economics reconsidered: Capacity limitation, entry and collusion," International Journal of Industrial Organization, Elsevier, vol. 15(3), pages 349-368, May.
  11. Allen, Franklin & Faulhaber, Gerald R, 1991. "Rational Rationing," Economica, London School of Economics and Political Science, vol. 58(230), pages 189-98, May.
  12. 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.
  13. 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.
  14. Rees, Ray, 1993. "Collusive Equilibrium in the Great Salt Duopoly," Munich Reprints in Economics 3413, University of Munich, Department of Economics.
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  16. 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.
  17. 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 413-28, June.
  18. 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.
  19. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
  20. Svend Albæk & Peter Møllgaard & Per Baltzer Overgaard, 1997. "Government-Assisted Oligopoly Coordination? A Concrete Case," CIE Discussion Papers 1997-03, University of Copenhagen. Department of Economics. Centre for Industrial Economics.
  21. 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.
  22. Natalia Fabra, 2003. "Tacit Collusion in Repeated Auctions: Uniform Versus Discriminatory," Journal of Industrial Economics, Wiley Blackwell, vol. 51(3), pages 271-293, 09.
  23. 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.
  24. Rees, Ray, 1993. "Collusive Equilibrium in the Great Salt Duopoly," Economic Journal, Royal Economic Society, vol. 103(419), pages 833-48, July.
  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. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
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Citations

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Cited by:
  1. 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.
  2. Dechenaux, Emmanuel & Kovenock, Dan, 2005. "Tacit Collusion and Capacity Withholding in Repeated Uniform Price Auctions," Purdue University Economics Working Papers 1174, Purdue University, Department of Economics.
  3. Puzzello, Daniela, 2007. "Tie-Breaking Rules and Divisibility in Experimental Duopoly Markets," MPRA Paper 6436, University Library of Munich, Germany.
  4. 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.
  5. 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.
  6. 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).
  7. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  8. Dechenaux, Emmanuel & Kovenock, Dan, 2003. "Endogenous Rationing, Price Dispersion, and Collusion in Capacity Constrained Supergames," Purdue University Economics Working Papers 1164, Purdue University, Department of Economics.

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