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The strategic Marshallian cross

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  • Dickson, Alex
  • Hartley, Roger

Abstract

We prove existence and uniqueness of non-autarkic equilibria in bilateral oligopoly assuming only that preferences are binormal and satisfy a weakened version of gross substitutes. We permit complete heterogeneity of preferences and our analysis exploits the fact that payoffs depend only on own strategy and two universal aggregates. This allows us to define strategic versions of supply and demand curves such that non-autarkic Nash equilibria are in 1-1 correspondence with intersections of these curves. The same approach can be used to establish comparative statics under the assumptions above. As examples, we focus on adding players and changing endowments. This competitive approach also allows us to conclude that much of conventional Marshallian analysis is robust to strategic manipulation.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 64 (2008)
Issue (Month): 2 (November)
Pages: 514-532

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Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:514-532

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Web page: http://www.elsevier.com/locate/inca/622836

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Keywords: Strategic Marshallian cross Strategic manipulation Imperfect competition;

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References

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  1. Hartley, Roger & Richard Cornes, 2003. "Joint Production Games with Mixed Sharing Rules," Royal Economic Society Annual Conference 2003 99, Royal Economic Society.
  2. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer, vol. 26(4), pages 923-946, November.
  3. BLOCH, Francis & GHOSAL, Sayantan, 1994. "Stable Trading Structures in Bilateral Oligopolies," CORE Discussion Papers 1994056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Peck, James & Shell, Karl & Spear, Stephen E., 1992. "The market game: existence and structure of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 21(3), pages 271-299.
  5. Vives, Xavier, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," Review of Economic Studies, Wiley Blackwell, vol. 54(1), pages 87-103, January.
  6. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
  7. Dubey, Pradeep & Shubik, Martin, 1978. "A theory of money and financial institutions. 28. The non-cooperative equilibria of a closed trading economy with market supply and bidding strategies," Journal of Economic Theory, Elsevier, vol. 17(1), pages 1-20, February.
  8. Cornes, Richard & Hartley, Roger, 2003. " Risk Aversion, Heterogeneity and Contests," Public Choice, Springer, vol. 117(1-2), pages 1-25, October.
  9. Novshek, William, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 85-98, January.
  10. 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.
  11. Bloch, Francis & Ferrer, Helene, 2001. "Trade Fragmentation and Coordination in Strategic Market Games," Journal of Economic Theory, Elsevier, vol. 101(1), pages 301-316, November.
  12. Rabah Amir & Siddhartha Sahi & Martin Shubik, 1986. "A Strategic Market Game with Complete Markets," Cowles Foundation Discussion Papers 814R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  13. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
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Citations

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Cited by:
  1. Alex Dickson & Roger Hartley, 2009. "Bilateral oligopoly and quantity competition," Working Papers 0922, University of Strathclyde Business School, Department of Economics.
  2. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, Open Access Journal, vol. 4(3), pages 283-303, June.
  3. Dickson Alex, 2013. "Cobb-Douglas preferences in bilateral oligopoly," Working Papers 1306, University of Strathclyde Business School, Department of Economics.
  4. Richard Cornes & Roger Hartley & Yuji Tamura, 2010. "A New Approach to Solving Production-Appropriation Games with Many Heterogeneous Players," ANU Working Papers in Economics and Econometrics 2010-521, Australian National University, College of Business and Economics, School of Economics.

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