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Bilateral oligopoly and quantity competition

  • Alex Dickson
  • Roger Hartley

Bilateral oligopoly is a market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, bilateral oligopoly 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 and investigate the differences in equilibria otherwise. These results lead to necessary and sufficient 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. Copyright Springer-Verlag 2013

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Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 0911.

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Date of creation: 2009
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Handle: RePEc:man:sespap:0911
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Web page: http://www.socialsciences.manchester.ac.uk/subjects/economics/

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  1. Novshek, William., 1984. "On the Existence of Cournot Equilibrium," Working Papers 517, California Institute of Technology, Division of the Humanities and Social Sciences.
  2. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, June.
  3. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," CORE Discussion Papers 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. 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.
  5. Richard Cornes & Roger Hartley, 2002. "Asymmetric Contests with General Technologies," Keele Economics Research Papers KERP 2002/22, Centre for Economic Research, Keele University.
  6. 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.
  7. R Cornes & R Hartley, 2005. "The Geometry of Aggregative Games," The School of Economics Discussion Paper Series 0514, Economics, The University of Manchester.
  8. Alex Dickson & Roger Hartley, 2007. "The strategic Marshallian cross," Keele Economics Research Papers KERP 2007/13, Centre for Economic Research, Keele University.
  9. 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.
  10. Stein, William E, 2002. " Asymmetric Rent-Seeking with More Than Two Contestants," Public Choice, Springer, vol. 113(3-4), pages 325-36, December.
  11. 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.
  12. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  13. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
  14. Codognato, Giulio, 1995. "Cournot-Walras and Cournot Equilibria in Mixed Markets: A Comparison," Economic Theory, Springer, vol. 5(2), pages 361-70, March.
  15. 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.
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