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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.
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    File URL: http://www.keele.ac.uk/depts/ec/wpapers/kerp0713.pdf
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    Citations

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    Cited by:

    1. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    2. 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.
    3. Anicet Kabre, 2018. "Cobb-Douglas preferences and pollution in a bilateral oligopoly market," Working Papers hal-04141683, HAL.
    4. 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.
    5. Ludovic A. Julien & Gagnie Pascal Yebarth, 2024. "Pareto-Optimal Taxation Mechanism in Noncooperative Strategic Bilateral Exchange," Working Papers hal-04604299, HAL.
    6. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, vol. 4(3), pages 1-21, June.
    7. 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.
    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, 2024. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 325-371, June.
    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. Ludovic A. Julien, 2017. "Hierarchical competition and heterogeneous behavior in noncooperative oligopoly markets," Working Papers hal-04141649, HAL.
    14. Anicet Kabre, 2018. "Cobb-Douglas preferences and pollution in a bilateral oligopoly market," EconomiX Working Papers 2018-48, University of Paris Nanterre, EconomiX.
    15. 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.
    16. 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.
    17. repec:rnp:ecopol:1539 is not listed on IDEAS
    18. Alex Dickson, 2017. "Multiple-aggregate games," Working Papers 1701, University of Strathclyde Business School, Department of Economics.

    More about this item

    Keywords

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    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

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