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Dynamic price competition with capacity constraints and strategic buyers

Author

Listed:
  • Gary Biglaiser

    (University of North Carolina)

  • Nikolaos Vettas

    (Athens University of Economics and Business)

Abstract

We analyze a dynamic durable good oligopoly model where sellers are capacity constrained over the length of the game. Buyers act strategically in the market, knowing that their purchases may affect future prices. The model is examined when there is one and multiple buyers. Sellers choose their capacities at the start of the game. We find that there are only mixed strategy equilibria. Buyers may split orders, preferring to buy a unit from both high and low price sellers to buying all units from the low price seller. Sellers enjoy a rent above the amount needed to satisfy the market demand that the other seller cannot meet. Buyers would like to commit not to buy in the future or hire agents with instructions to always buy from the lowest priced seller. Further, sellers’ market shares tend to be asymmetric with high probability, even though they are ex ante identical.

Suggested Citation

  • Gary Biglaiser & Nikolaos Vettas, 2007. "Dynamic price competition with capacity constraints and strategic buyers," Working Papers 24, Portuguese Competition Authority.
    • Handle: RePEc:pca:wpaper:24
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    1. Val Eugene Lambson, 1987. "Optimal Penal Codes in Price-setting Supergames with Capacity Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 385-397.
    2. David Besanko & Ulrich Doraszelski, 2004. "Capacity Dynamics and Endogenous Asymmetries in Firm Size," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 23-49, Spring.
    3. Carl Davidson & Raymond Deneckere, 1986. "Long-Run Competition in Capacity, Short-Run Competition in Price, and the Cournot Model," RAND Journal of Economics, The RAND Corporation, vol. 17(3), pages 404-415, Autumn.
    4. Bloch, Francis & Ghosal, Sayantan, 1997. "Stable Trading Structures in Bilateral Oligopolies," Journal of Economic Theory, Elsevier, vol. 74(2), pages 368-384, June.
    5. 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.
    6. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    7. Reynolds, Stanley S. & Wilson, Bart J., 2000. "Bertrand-Edgeworth Competition, Demand Uncertainty, and Asymmetric Outcomes," Journal of Economic Theory, Elsevier, vol. 92(1), pages 122-141, May.
    8. Saloner, Garth, 1987. "Cournot duopoly with two production periods," Journal of Economic Theory, Elsevier, vol. 42(1), pages 183-187, June.
    9. 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.
    10. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, September.
    11. Kirman, Alan P & Sobel, Matthew J, 1974. "Dynamic Oligopoly with Inventories," Econometrica, Econometric Society, vol. 42(2), pages 279-287, March.
    12. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    13. Pankaj Ghemawat, 1997. "Games Businesses Play: Cases and Models," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262071827, April.
    14. Bergemann, Dirk & Valimaki, Juuso, 1996. "Learning and Strategic Pricing," Econometrica, Econometric Society, vol. 64(5), pages 1125-1149, September.
    15. Dixit, Avinash, 1980. "The Role of Investment in Entry-Deterrence," Economic Journal, Royal Economic Society, vol. 90(357), pages 95-106, March.
    16. Dirk Bergemann & Juuso Välimäki, 2000. "Experimentation in Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(2), pages 213-234.
    17. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    18. Henrick Horn & Asher Wolinsky, 1988. "Bilateral Monopolies and Incentives for Merger," RAND Journal of Economics, The RAND Corporation, vol. 19(3), pages 408-419, Autumn.
    19. Maskin, Eric & Tirole, Jean, 1988. "A Theory of Dynamic Oligopoly, II: Price Competition, Kinked Demand Curves, and Edgeworth Cycles," Econometrica, Econometric Society, vol. 56(3), pages 571-599, May.
    20. Stennek, Johan & Björnerstedt, Jonas, 2001. "Bilateral Oligopoly," CEPR Discussion Papers 2864, C.E.P.R. Discussion Papers.
    21. Spulber, Daniel F, 1981. "Capacity, Output, and Sequential Entry," American Economic Review, American Economic Association, vol. 71(3), pages 503-514, June.
    22. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    23. Jean J. Gabszewicz & Sougata Poddar, 1997. "Demand fluctuations and capacity utilization under duopoly," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 131-146.
    24. Garcia, Alfredo & Reitzes, James D & Stacchetti, Ennio, 2001. "Strategic Pricing when Electricity is Storable," Journal of Regulatory Economics, Springer, vol. 20(3), pages 223-247, November.
    25. 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.
    26. Dobson, Paul W & Waterson, Michael, 1997. "Countervailing Power and Consumer Prices," Economic Journal, Royal Economic Society, vol. 107(441), pages 418-430, March.
    27. James J. Anton & Dennis A. Yao, 1992. "Coordination in Split Award Auctions," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(2), pages 681-707.
    28. James J. Anton & Dennis A. Yao, 1989. "Split Awards, Procurement, and Innovation," RAND Journal of Economics, The RAND Corporation, vol. 20(4), pages 538-552, Winter.
    29. Willis R. Greer, Jr. & Shu S. Liao, 1986. "An Analysis of Risk and Return in the Defense Market: Its Impact on Weapon System Competition," Management Science, INFORMS, vol. 32(10), pages 1259-1273, October.
    30. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 27-41.
    31. Cabral, Luis M B & Riordan, Michael H, 1994. "The Learning Curve, Market Dominance, and Predatory Pricing," Econometrica, Econometric Society, vol. 62(5), pages 1115-1140, September.
    32. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    33. Marc Dudey, 1992. "Dynamic Edgeworth-Bertrand Competition," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1461-1477.
    34. Roman Inderst, 2008. "Single sourcing versus multiple sourcing," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 199-213, March.
    35. Giovanni Maggi, 1996. "Endogenous Leadership in a New Market," RAND Journal of Economics, The RAND Corporation, vol. 27(4), pages 641-659, Winter.
    36. Inderst, Roman & Wey, Christian, 2003. "Bargaining, Mergers, and Technology Choice in Bilaterally Oligopolistic Industries," RAND Journal of Economics, The RAND Corporation, vol. 34(1), pages 1-19, Spring.
    37. James J. Anton & Dennis A. Yao, 1987. "Second Sourcing and the Experience Curve: Price Competition in Defense Procurement," RAND Journal of Economics, The RAND Corporation, vol. 18(1), pages 57-76, Spring.
    38. Kevin Lang & Robert W. Rosenthal, 1991. "The Contractors' Game," RAND Journal of Economics, The RAND Corporation, vol. 22(3), pages 329-338, Autumn.
    39. Compte, Olivier & Jenny, Frederic & Rey, Patrick, 2002. "Capacity constraints, mergers and collusion," European Economic Review, Elsevier, vol. 46(1), pages 1-29, January.
    40. Julio J. Rotemberg & Garth Saloner, 1989. "The Cyclical Behavior of Strategic Inventories," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(1), pages 73-97.
    41. William A. Brock & José A. Scheinkman, 1985. "Price Setting Supergames with Capacity Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(3), pages 371-382.
    42. Ching‐To Albert Ma, 1997. "Option Contracts and Vertical Foreclosure," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 6(4), pages 725-753, December.
    43. Tracy R. Lewis & Huseyin Yildirim, 2002. "Managing Dynamic Competition," American Economic Review, American Economic Association, vol. 92(4), pages 779-797, September.
    44. Riordan, Michael H & Sappington, David E M, 1987. "Awarding Monopoly Franchises," American Economic Review, American Economic Association, vol. 77(3), pages 375-387, June.
    45. Rob, Rafael, 1986. "The Design of Procurement Contracts," American Economic Review, American Economic Association, vol. 76(3), pages 378-389, June.
    46. repec:hhs:iuiwop:555 is not listed on IDEAS
    47. James J. Anton & Dennis A. Yao, 1990. "Measuring the effectiveness of competition in defense procurement: A survey of the empirical literature," Journal of Policy Analysis and Management, John Wiley & Sons, Ltd., vol. 9(1), pages 60-79.
    48. Björnerstedt, Jonas & Stennek, Johan, 2001. "Bilateral Oligopoly," Working Paper Series 555, Research Institute of Industrial Economics.
    49. 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.
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    Citations

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    Cited by:

    1. Vettas, Nikolaos & Kotseva, Rossitsa & Christou, Charalambos, 2007. "Pricing, Investments and Mergers with Intertemporal Capacity Constraints," CEPR Discussion Papers 6433, C.E.P.R. Discussion Papers.
    2. Fabian Bergès & Claire Chambolle, 2009. "Threat of Exit as a Source of Bargaining Power," Recherches économiques de Louvain, De Boeck Université, vol. 75(3), pages 353-368.
    3. Berk, Istemi, 2015. "Two-Period Resource Duopoly with Endogenous Intertemporal Capacity Constraints," EWI Working Papers 2014-13, Energiewirtschaftliches Institut an der Universitaet zu Koeln (EWI).
    4. Liski, Matti & Montero, Juan-Pablo, 2014. "Forward trading in exhaustible-resource oligopoly," Resource and Energy Economics, Elsevier, vol. 37(C), pages 122-146.
    5. van den Berg, A.H.J. & Herings, P.J.J. & Peters, H.J.M., 2009. "Dynamic duopoly with intertemporal capacity constraints," Research Memorandum 018, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Vettas, Nikolaos & Biglaiser, Gary, 2004. "Dynamic Price Competition with Capacity Constraints and Strategic Buyers," CEPR Discussion Papers 4315, C.E.P.R. Discussion Papers.
    7. E. Bacchiega & O. Bonroy, 2012. "Vertical relations and number of channels in quality-differentiated markets," Working Papers wp823, Dipartimento Scienze Economiche, Universita' di Bologna.
    8. Sakellaris, Kostis, 2010. "Modeling Electricity Markets as Two-Stage Capacity Constrained Price Competition Games under Uncertainty," MPRA Paper 23317, University Library of Munich, Germany.
    9. Kalyan Talluri & Victor Martínez-de-Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona School of Economics.
    10. van den Berg, Anita & Bos, Iwan & Herings, P. Jean-Jacques & Peters, Hans, 2012. "Dynamic Cournot duopoly with intertemporal capacity constraints," International Journal of Industrial Organization, Elsevier, vol. 30(2), pages 174-192.
    11. Victor Martínez-de-Albéniz & Kalyan Talluri, 2011. "Dynamic Price Competition with Fixed Capacities," Management Science, INFORMS, vol. 57(6), pages 1078-1093, June.
    12. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic price competition with fixed capacities," Economics Working Papers 1205, Department of Economics and Business, Universitat Pompeu Fabra.
    13. Niloofar Fadavi, 2022. "Subgame perfect Nash equilibrium for dynamic pricing competition with finite planning horizon," Papers 2208.02842, arXiv.org.
    14. James J. Anton & Gary Biglaiser & Nikolaos Vettas, 2014. "Dynamic Price Competition With Capacity Constraints And A Strategic Buyer," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 943-958, August.
    15. Bhaskar, Venkataraman, 2013. "Dynamic Countervailing Power under Public and Private Monitoring," CEPR Discussion Papers 9526, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    Strategic buyers; capacity constraints; bilateral oligopoly; dynamic competition;
    All these keywords.

    JEL classification:

    • D4 - Microeconomics - - Market Structure, Pricing, and Design
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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