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Price and Capacity Competition

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  • Daron Acemoglu
  • Kostas Bimpikis
  • Asuman Ozdaglar

Abstract

We study the efficiency of oligopoly equilibria in a model where firms compete over capacities and prices. The motivating example is a communication network where service providers invest in capacities and then compete in prices. Our model economy corresponds to a two-stage game. First, firms (service providers) independently choose their capacity levels. Second, after the capacity levels are observed, they set prices. Given the capacities and prices, users (consumers) allocate their demands across the firms. We first establish the existence of pure strategy subgame perfect equilibria (oligopoly equilibria) and characterize the set of equilibria. These equilibria feature pure strategies along the equilibrium path, but off-the-equilibrium path they are supported by mixed strategies. We then investigate the efficiency properties of these equilibria, where "efficiency" is defined as the ratio of surplus in equilibrium relative to the first best. We show that efficiency in the worst oligopoly equilibria of this game can be arbitrarily low. However, if the best oligopoly equilibrium is selected (among multiple equilibria), the worst-case efficiency loss has a tight bound, approximately equal to 5/6 with 2 firms. This bound monotonically decreases towards zero when the number of firms increases. We also suggest a simple way of implementing the best oligopoly equilibrium. With two firms, this involves the lower-cost firm acting as a Stackelberg leader and choosing its capacity first. We show that in this Stackelberg game form, there exists a unique equilibrium corresponding to the best oligopoly equilibrium. We also show that an alternative game form where capacities and prices are chosen simultaneously always fails to have a pure strategy equilibrium. These results suggest that the timing of capacity and price choices in oligopolistic environments is important both for the existence of equilibrium and for the extent of efficiency losses in equilibrium.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 12804.

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Date of creation: Dec 2006
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Publication status: published as Acemoglu, Daron & Bimpikis, Kostas & Ozdaglar, Asuman, 2009. "Price and capacity competition," Games and Economic Behavior, Elsevier, vol. 66(1), pages 1-26, May.
Handle: RePEc:nbr:nberwo:12804

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  1. Daron Acemoglu & Asuman Ozdaglar, 2005. "Competition and Efficiency in Congested Markets," NBER Working Papers 11201, National Bureau of Economic Research, Inc.
  2. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  3. Richard E. Levitan & Martin Shubik, 1970. "Duopoly with Price and Quantity as Strategic Variables," Cowles Foundation Discussion Papers 289, Cowles Foundation for Research in Economics, Yale University.
  4. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  5. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
  6. Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006. "Designing electricity auctions," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 23-46, 03.
  7. 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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Cited by:
  1. van den Berg, Vincent A.C. & Verhoef, Erik T., 2012. "Is the travel time of private roads too short, too long, or just right?," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 971-983.
  2. Robert Somogyi, 2013. "Bertrand-Edgeworth competition with substantial product differentiation," IEHAS Discussion Papers 1332, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
  3. Vincent A.C. van den Berg, 2012. "Auctions for Private Congestible Infrastructures," Tinbergen Institute Discussion Papers 12-087/VIII, Tinbergen Institute, revised 19 Oct 2012.
  4. José R. Correa & Nicolás Figueroa & Nicolás E. Stier-Moses, 2008. "Pricing with markups in industries with increasing marginal costs," Documentos de Trabajo 256, Centro de Economía Aplicada, Universidad de Chile.
  5. repec:dgr:uvatin:2012087 is not listed on IDEAS
  6. Liu, Tian-Liang & Chen, Jian & Huang, Hai-Jun, 2011. "Existence and efficiency of oligopoly equilibrium under toll and capacity competition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(6), pages 908-919.
  7. van den Berg, Vincent A.C., 2013. "Serial private infrastructures," Transportation Research Part B: Methodological, Elsevier, vol. 56(C), pages 186-202.
  8. 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.

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