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Bertrand Competition with Subcontracting


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  • Morton I. Kamien
  • Lode Li
  • Dov Samet


We investigate how the possibility of subsequently subcontracting production to each other influences rivals' initial competition for a contract or a market as a two-stage game. In its first stage, the two firms engage in price competition to supply a contract or a market. In the second stage, the firms may subcontract production to each other. It is supposed that the firms produce the identical product with the same strictly convex cost function. The incentive for subcontracting comes from the strictly convex production costs. A firm is obliged to supply the entire quantity demanded at its quoted price. Our analysis discloses that if the winner of the game's first stage determines the terms of the subcontract in its second stage, there exists a unique, subgame perfect Nash equilibrium (SPNE) in pure strategies in which the firms bid the same price in the first stage and both receive zero profits. On the other hand, if the loser of the game's first stage sets the terms of the subcontract in the second stage, there exists a unique SPNE in pure strategies in which the firms bid the same price in the first stage and both receive positive profits. The presence of the possibility of subcontracting supports a unique SPNE in pure strategies, even though no actual subcontracting may occur. The SPNE price is below the socially-optimal price in the first case and is above it in the second case. We also consider other modes of sharing the gains from subcontracting between the two firms, such as the Nash bargaining solution.

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Bibliographic Info

Article provided by The RAND Corporation in its journal RAND Journal of Economics.

Volume (Year): 20 (1989)
Issue (Month): 4 (Winter)
Pages: 553-567

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Handle: RePEc:rje:randje:v:20:y:1989:i:winter:p:553-567

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Cited by:
  1. Marechal, Francois & Morand, Pierre-Henri, 2003. "Pre vs. post-award subcontracting plans in procurement bidding," Economics Letters, Elsevier, Elsevier, vol. 81(1), pages 23-30, October.
  2. Charles Zheng, 2000. "An Optimal Auction When Resale Cannot Be Prohibited," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 1303, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Hans-Theo Normann, 2001. "Exchange Agreements Facilitate Collusion," German Economic Review, Verein für Socialpolitik, Verein für Socialpolitik, vol. 2(2), pages 113-125, 05.
  4. Veronika Grimm, 2004. "On Procurement Auctions Of Complementary Goods," Working Papers. Serie AD, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie) 2004-02, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Wambach, Achim, 2009. "How to subcontract?," Economics Letters, Elsevier, Elsevier, vol. 105(2), pages 152-155, November.
  6. Veronika Grimm, 2007. "Sequential versus Bundle Auctions for Recurring Procurement," Journal of Economics, Springer, Springer, vol. 90(1), pages 1-27, January.
  7. Bernard Lebrun, 2008. "First-Price, Second-Price, and English Auctions with Resale," Working Papers, York University, Department of Economics 2008_06, York University, Department of Economics.
  8. Luigi Moretti & Paola Valbonesi, 2012. "Subcontracting in Public Procurement: An Empirical Investigation," "Marco Fanno" Working Papers, Dipartimento di Scienze Economiche "Marco Fanno" 0154, Dipartimento di Scienze Economiche "Marco Fanno".
  9. Arya, Anil & Mittendorf, Brian & Sappington, David E.M., 2008. "Outsourcing, vertical integration, and price vs. quantity competition," International Journal of Industrial Organization, Elsevier, Elsevier, vol. 26(1), pages 1-16, January.
  10. Frode Meland & Odd Straume, 2007. "Outsourcing in contests," Public Choice, Springer, Springer, vol. 131(3), pages 315-331, June.
  11. De Frutos, María Ángeles & Espinosa Alejos, María Paz, 2012. "Resale in Auctions with Financial Constraints," DFAEII Working Papers 2012-03, University of the Basque Country - Department of Foundations of Economic Analysis II.
  12. Shy, Oz & Stenbacka, Rune, 2003. "Strategic outsourcing," Journal of Economic Behavior & Organization, Elsevier, Elsevier, vol. 50(2), pages 203-224, February.
  13. Liang, Wen-Jung & Mai, Chao-Cheng, 2006. "Validity of the principle of minimum differentiation under vertical subcontracting," Regional Science and Urban Economics, Elsevier, Elsevier, vol. 36(3), pages 373-384, May.
  14. Haile, Philip A., 2003. "Auctions with private uncertainty and resale opportunities," Journal of Economic Theory, Elsevier, Elsevier, vol. 108(1), pages 72-110, January.
  15. Liang, Xiaoying & Xie, Lei & Yan, Houmin, 2012. "Bertrand competition with intermediation," Economics Letters, Elsevier, Elsevier, vol. 116(1), pages 112-114.
  16. Joaquín Andaluz, 2008. "Vertical product differentiation with subcontracting," Documentos de Trabajo, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza dt2008-01, Facultad de Ciencias Económicas y Empresariales, Universidad de Zaragoza.


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