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Cobb-Douglas preferences in bilateral oligopoly

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  • Dickson Alex

    ()
    (Department of Economics, University of Strathclyde)

Abstract

Bilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two ‘partial games’. First, fix the aggregate bid at B; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is X˜ (B). Next, fix the aggregate supply at X; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is ˜B (X). The analysis of these two partial games takes into account competition within each side of the market. Equilibrium in bilateral oligopoly must take into account competition between sellers and buyers and requires, for example, ˜B (X˜ (B)) = B. When all traders have Cobb-Douglas preferences ˜ X(B) does not depend on B and ˜B (X) does not depend on X: whilst there is competition within each side of the market there is no strategic interdependence between the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated.

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Bibliographic Info

Paper provided by University of Strathclyde Business School, Department of Economics in its series Working Papers with number 1306.

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Length: 21 pages
Date of creation: Jun 2013
Date of revision:
Publication status: Published
Handle: RePEc:str:wpaper:1306

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Keywords: strategic market game; bilateral oligopoly; Cobb-Douglas preferences;

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References

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  1. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
  2. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
  3. Busetto, Francesca & Codognato, Giulio, 2006. ""Very Nice" trivial equilibria in strategic market games," Journal of Economic Theory, Elsevier, vol. 131(1), pages 295-301, November.
  4. Richard Cornes & Roger Hartley, 2002. "Asymmetric Contests with General Technologies," Keele Economics Research Papers KERP 2002/22, Centre for Economic Research, Keele University.
  5. 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.
  6. Alex Dickson & Roger Hartley, 2013. "On ‘Nice’ And ‘Very Nice’ Autarkic Equilibria In Strategic Market Games," Manchester School, University of Manchester, vol. 81(5), pages 745-762, 09.
  7. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, Open Access Journal, vol. 4(3), pages 283-303, June.
  8. Alex Dickson & Roger Hartley, 2009. "Bilateral oligopoly and quantity competition," Working Papers 0922, University of Strathclyde Business School, Department of Economics.
  9. 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.
  10. Perez-Castrillo, J David & Verdier, Thierry, 1992. " A General Analysis of Rent-Seeking Games," Public Choice, Springer, vol. 73(3), pages 335-50, April.
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