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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. Brock, William A & Scheinkman, Jose A, 1985. "Price Setting Supergames with Capacity Constraints," Review of Economic Studies, Wiley Blackwell, vol. 52(3), pages 371-82, July.
  2. Sorgard, L., 1995. "Judo Economics Reconsidered: Capacity Limitation, Entry and Collusion," Papers 18/95, Norwegian School of Economics and Business Administration-.
  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.
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  6. Emmanuel Dechenaux & Dan Kovenock, 2011. "Endogenous rationing, price dispersion and collusion in capacity constrained supergames," Economic Theory, Springer, vol. 47(1), pages 29-74, May.
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  24. Davidson, Carl & Deneckere, Raymond, 1984. "Horizontal mergers and collusive behavior," International Journal of Industrial Organization, Elsevier, vol. 2(2), pages 117-132, June.
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Citations

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Cited by:
  1. 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.
  2. Christopher Knittel & Jason Lepore, 2006. "Tacit Collusion in the Presence of Cyclical Demand and Endogenous Capacity Levels," Working Papers 631, University of California, Davis, Department of Economics.
  3. 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.
  4. 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.
  5. Dechenaux, Emmanuel & Kovenock, Dan, 2007. "Tacit collusion and capacity withholding in repeated uniform price auctions," MPRA Paper 36764, University Library of Munich, Germany.
  6. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer, vol. 46(1), pages 99-125, January.
  7. Puzzello, Daniela, 2006. "Tie-Breaking Rules and Divisibility in Experimental Duopoly Markets," MPRA Paper 6453, University Library of Munich, Germany.
  8. 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).

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