IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v64y2008i2p514-532.html
   My bibliography  Save this article

The strategic Marshallian cross

Author

Listed:
  • 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.

Suggested Citation

  • Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
  • Handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:514-532
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00047-X
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Richard Cornes & Roger Hartley, 2002. "Joint Production Games with Mixed Sharing Rules," Keele Economics Research Papers KERP 2002/16, Centre for Economic Research, Keele University.
    2. Richard Cornes & Roger Hartley, 2005. "Asymmetric contests with general technologies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 923-946, November.
    3. Bloch, Francis & Ghosal, Sayantan, 1997. "Stable Trading Structures in Bilateral Oligopolies," Journal of Economic Theory, Elsevier, vol. 74(2), pages 368-384, June.
    4. Amir, Rabah & Sahi, Siddharta & Shubik, Martin & Yao, Shuntian, 1990. "A strategic market game with complete markets," Journal of Economic Theory, Elsevier, vol. 51(1), pages 126-143, June.
    5. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    6. 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.
    7. 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.
    8. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    9. repec:cor:louvrp:-1265 is not listed on IDEAS
    10. 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.
    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 937-968, October.
    12. Cornes, Richard & Hartley, Roger, 2003. "Risk Aversion, Heterogeneity and Contests," Public Choice, Springer, vol. 117(1-2), pages 1-25, October.
    13. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    14. Xavier Vives, 1987. "Small Income Effects: A Marshallian Theory of Consumer Surplus and Downward Sloping Demand," Review of Economic Studies, Oxford University Press, vol. 54(1), pages 87-103.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Roy H Grieve, 2013. "An issue with own-rates: Keynes borrows from Sraffa , Sraffa criticises Keynes, and present-day commentators get hold of the wrong end of the stick," Working Papers 1319, University of Strathclyde Business School, Department of Economics.
    2. 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.
    3. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    4. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic A. Julien & Simone Tonin, 2018. "Existence and Optimality of Cournot-Nash Equilibria in a Bilateral Oligopoly with Atoms and an Atomless Part," EconomiX Working Papers 2018-10, University of Paris Nanterre, EconomiX.
    5. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, Open Access Journal, vol. 4(3), pages 1-21, June.
    6. repec:eee:gamebe:v:108:y:2018:i:c:p:478-485 is not listed on IDEAS
    7. Alex Dickson and & Roger Hartley, 2006. "On a foundation for Cournot equilibrium," The School of Economics Discussion Paper Series 0638, Economics, The University of Manchester.
    8. Alex Dickson, 2010. "The effects of entry in thin markets," Working Papers 1011, University of Strathclyde Business School, Department of Economics.
    9. Alex Dickson & Ian A. MacKenzie & Petros G. Sekeris, 2016. "Sharing contests with general preferences," Discussion Papers Series 573, School of Economics, University of Queensland, Australia.
    10. Cont, Walter & Porto, Guido, 2014. "Measuring the impact of a change in the price of Cashew received by exporters on farmgate prices and poverty in Guinea-Bissau," Policy Research Working Paper Series 7036, The World Bank.
    11. Alex Dickson, 2013. "On Cobb-Douglas Preferences in Bilateral Oligopoly," Recherches économiques de Louvain, De Boeck Université, vol. 79(4), pages 89-110.
    12. Dickson, Alex & MacKenzie, Ian A., 2018. "Strategic trade in pollution permits," Journal of Environmental Economics and Management, Elsevier, vol. 87(C), pages 94-113.
    13. Dickson Alex, 2013. "Cobb-Douglas preferences in bilateral oligopoly," Working Papers 1306, University of Strathclyde Business School, Department of Economics.
    14. Dickson, Alex & Hartley, Roger, 2011. "Trade in bilateral oligopoly with endogenous market formation," SIRE Discussion Papers 2011-12, Scottish Institute for Research in Economics (SIRE).
    15. Alex Dickson & Roger Hartley, 2013. "Bilateral oligopoly and quantity competition," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(3), pages 979-1004, April.
    16. Alex Dickson, 2017. "Multiple-aggregate games," Working Papers 1701, University of Strathclyde Business School, Department of Economics.
    17. Ludovic Alexandre Julien, 2017. "Hierarchical competition and heterogeneous behavior in noncooperative oligopoly markets," EconomiX Working Papers 2017-22, University of Paris Nanterre, EconomiX.
    18. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan & Julien, Ludovic & Tonin, Simone, 2018. "Noncooperative oligopoly in markets with a continuum of traders and a strongly connected set of commodities," Games and Economic Behavior, Elsevier, vol. 108(C), pages 478-485.

    More about this item

    Keywords

    Strategic Marshallian cross Strategic manipulation Imperfect competition;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:64:y:2008:i:2:p:514-532. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.