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Bilateral oligopoly and quantity competition

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  • Alex Dickson

    ()
    (Department of Economics, University of Strathclyde)

  • Roger Hartley

    ()
    (Department of Economics, University of Manchester)

Abstract

Bilateral oligopoly is a strategic market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, such a game approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one. These results lead to necessary and su¢ cient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied.

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Bibliographic Info

Paper provided by University of Strathclyde Business School, Department of Economics in its series Working Papers with number 0922.

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Length: 28 pages
Date of creation: Oct 2009
Date of revision:
Handle: RePEc:str:wpaper:0922

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Keywords: Quantity competition; Cournot; strategic foundation; commitmen;

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References

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  1. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer, vol. 26(4), pages 923-946, November.
  2. Shapley, Lloyd S & Shubik, Martin, 1977. "Trade Using One Commodity as a Means of Payment," Journal of Political Economy, University of Chicago Press, vol. 85(5), pages 937-68, October.
  3. JASKOLD GABSZEWICZ, Jean & VIAL, Jean-Philippe, . "Oligopoly "à la Cournot" in a general equilibrium analysis," CORE Discussion Papers RP -106, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  5. Alex Dickson & Roger Hartley, 2007. "The strategic Marshallian cross," Keele Economics Research Papers KERP 2007/13, Centre for Economic Research, Keele University.
  6. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, December.
  7. Szidarovszky, F & Yakowitz, S, 1977. "A New Proof of the Existence and Uniqueness of the Cournot Equilibrium," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 787-89, October.
  8. Gabszewicz, J.J. & Michel, P., . "Oligopoly equilibrium in exchange economies," CORE Discussion Papers RP -1265, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Stein, William E, 2002. " Asymmetric Rent-Seeking with More Than Two Contestants," Public Choice, Springer, vol. 113(3-4), pages 325-36, December.
  10. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  11. Codognato, Giulio, 1995. "Cournot-Walras and Cournot Equilibria in Mixed Markets: A Comparison," Economic Theory, Springer, vol. 5(2), pages 361-70, March.
  12. 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.
  13. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," The School of Economics Discussion Paper Series 0514, Economics, The University of Manchester.
  14. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
  15. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2008. "Cournot-Walras Equilibrium as a Subgame Perfect Equilibrium," The Warwick Economics Research Paper Series (TWERPS) 837, University of Warwick, Department of Economics.
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Cited by:
  1. Richard Cornes & Roger Hartley & Yuji Tamura, 2010. "A New Approach to Solving Production-Appropriation Games with Many Heterogeneous Players," CESifo Working Paper Series 3060, CESifo Group Munich.
  2. Dickson Alex, 2013. "Cobb-Douglas preferences in bilateral oligopoly," Working Papers 1306, University of Strathclyde Business School, Department of Economics.

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