IDEAS home Printed from https://ideas.repec.org/p/kee/kerpuk/2007-13.html
   My bibliography  Save this paper

The strategic Marshallian cross

Author

Listed:
  • Alex Dickson

    (Keele University, Centre for Economic Research and School of Economic and Management Studies)

  • Roger Hartley

    (Department of Economics, University of Manchester)

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

  • Alex Dickson & Roger Hartley, 2007. "The strategic Marshallian cross," Keele Economics Research Papers KERP 2007/13, Centre for Economic Research, Keele University.
    • Handle: RePEc:kee:kerpuk:2007/13
    Note: This is the revised version of an earlier paper, first circulated as Keele Economics Research Paper 04/07 and University of Manchester Economics Discussion Paper 0523, under different titles.
    as

    Download full text from publisher

    File URL: http://www.keele.ac.uk/depts/ec/wpapers/kerp0713.pdf
    Download Restriction: no
    ---><---

    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. Bloch, Francis & Ghosal, Sayantan, 1997. "Stable Trading Structures in Bilateral Oligopolies," Journal of Economic Theory, Elsevier, vol. 74(2), pages 368-384, June.
    3. B. C. Eaton & Richard G. Harris (ed.), 1997. "Trade, Technology and Economics," Books, Edward Elgar Publishing, number 1020.
    4. William Novshek, 1985. "On the Existence of Cournot Equilibrium," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 85-98.
    5. 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.
    6. repec:cor:louvrp:-1265 is not listed on IDEAS
    7. 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.
    8. GABSZEWICZ, Jean & MICHEL, Philippe, 1992. "Oligopoly equilibria in exchange economies," LIDAM Discussion Papers CORE 1992047, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    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 937-968, October.
    10. 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.
    11. 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.
    12. 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.
    13. Corchon, Luis C., 1994. "Comparative statics for aggregative games the strong concavity case," Mathematical Social Sciences, Elsevier, vol. 28(3), pages 151-165, December.
    14. 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.
    15. Cornes, Richard & Hartley, Roger, 2003. "Risk Aversion, Heterogeneity and Contests," Public Choice, Springer, vol. 117(1-2), pages 1-25, October.
    16. Giraud, Gael, 2003. "Strategic market games: an introduction," Journal of Mathematical Economics, Elsevier, vol. 39(5-6), pages 355-375, July.
    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. Ludovic A. Julien, 2017. "Hierarchical competition and heterogeneous behavior in noncooperative oligopoly markets," Working Papers hal-04141649, HAL.
    2. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    3. Richard Cornes & Roger Hartley & Yuji Tamura, 2019. "Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model," Scandinavian Journal of Economics, Wiley Blackwell, vol. 121(1), pages 353-378, January.
    4. Anicet Kabre, 2018. "Cobb-Douglas preferences and pollution in a bilateral oligopoly market," Working Papers hal-04141683, HAL.
    5. 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.
    6. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    7. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, vol. 4(3), pages 1-21, June.
    8. 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.
    9. Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," Working Papers hal-04159741, HAL.
    10. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    11. Dickson, Alex & MacKenzie, Ian A., 2018. "Strategic trade in pollution permits," Journal of Environmental Economics and Management, Elsevier, vol. 87(C), pages 94-113.
    12. 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.
    13. Anicet Kabre, 2018. "Cobb-Douglas preferences and pollution in a bilateral oligopoly market," EconomiX Working Papers 2018-48, University of Paris Nanterre, EconomiX.
    14. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.
    15. M. Lombardi & S. Tonin, 2020. "On trade in bilateral oligopolies with altruistic and spiteful agents," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 203-218, October.
    16. Varshaver, Evgeniy (Варшавер, Евгений) & Kruglova, Ekaterina (Круглова, Екатерина), 2015. ""Coalition clinch" against the Islamic order: the dynamics of market institutions dispute resolution in Dagestan [«Коалиционный Клинч» Против Исламского Порядка: Динамика Рынка Институтов," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 3, pages 89-112.
    17. Alex Dickson, 2017. "Multiple-aggregate games," Working Papers 1701, University of Strathclyde Business School, Department of Economics.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. A. Dickson & R. Hartley, 2005. "The strategic Marshallian cross and bilateral oligopoly," Economics Discussion Paper Series 0523, Economics, The University of Manchester.
    2. Francesca Busetto & Giulio Codognato & Sayantan Ghosal & Ludovic Julien & Simone Tonin, 2020. "Existence and optimality of Cournot–Nash equilibria in a bilateral oligopoly with atoms and an atomless part," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(4), pages 933-951, December.
    3. Busetto, Francesca & Codognato, Giulio & Julien, Ludovic, 2020. "Atomic Leontievian Cournotian traders are always Walrasian," Games and Economic Behavior, Elsevier, vol. 122(C), pages 318-327.
    4. Ludovic A. Julien, 2017. "Hierarchical Competition and Heterogeneous Behavior in Noncooperative Oligopoly Markets," Post-Print hal-01637298, HAL.
    5. Alex Dickson & Simone Tonin, 2021. "An introduction to perfect and imperfect competition via bilateral oligopoly," Journal of Economics, Springer, vol. 133(2), pages 103-128, July.
    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. Amir, Rabah & Bloch, Francis, 2009. "Comparative statics in a simple class of strategic market games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 7-24, January.
    8. Régis Breton & Bertrand Gobillard, 2005. "Robustness of equilibrium price dispersion in finite market games," Post-Print halshs-00257207, HAL.
    9. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, vol. 4(3), pages 1-21, June.
    10. 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.
    11. BLOCH, Francis & FERRER, Hélène, 1999. "Trade fragmentation and coordination in bilateral oligopolies," LIDAM Discussion Papers CORE 1999008, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Ghosal, Sayantan & Tonin, Simone, 2014. "Non-Cooperative Asymptotic Oligopoly in Economies with Infinitely Many Commodities," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-23, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2012. "Noncooperative Oligopoly in Markets with a Continuum of Traders: A Limit Theorem," The Warwick Economics Research Paper Series (TWERPS) 994, University of Warwick, Department of Economics.
    14. Cornes, Richard & Hartley, Roger, 2012. "Fully aggregative games," Economics Letters, Elsevier, vol. 116(3), pages 631-633.
    15. Ludovic A. Julien & Fabrice Tricou, 2008. "Market Price Mechanisms and Stackelberg General Equilibria," Working Papers hal-04140726, HAL.
    16. Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," EconomiX Working Papers 2021-14, University of Paris Nanterre, EconomiX.
    17. M. Lombardi & S. Tonin, 2020. "On trade in bilateral oligopolies with altruistic and spiteful agents," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 203-218, October.
    18. Busetto, Francesca & Codognato, Giulio & Ghosal, Sayantan, 2011. "Noncooperative oligopoly in markets with a continuum of traders," Games and Economic Behavior, Elsevier, vol. 72(1), pages 38-45, May.
    19. Jean J. Gabszewicz & Lisa Grazzini, 1999. "Taxing Market Power," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(4), pages 475-497, October.
    20. Papadopoulos Konstantinos G., 2008. "Purchasing Power Parity with Strategic Markets," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-32, June.

    More about this item

    Keywords

    Strategic Marshallian cross; strategic manipulation; imperfect competition.;
    All these keywords.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:kee:kerpuk:2007/13. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin E. Diedrich (email available below). General contact details of provider: https://edirc.repec.org/data/dekeeuk.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.