[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/drm/wpaper/2021-14.html
   My bibliography  Save this paper

Noncooperative oligopoly equilibrium in markets with hierarchical competition

Author

Listed:
  • Ludovic A. Julien
Abstract
This paper deals with the existence of a non-cooperative sequential equilibrium in interrelated markets with heterogeneous atomic traders. Since this model features a rich set of strategic interactions, there are two kinds of problems associated with the existence of equilibrium. First, existence and uniqueness of followers' strategies are not guaranteed. Second, the no-trade equilibrium is always an equilibrium outcome. To overcome these two difficulties we consider a differentiable approach. We show that the set of equations which determines the strategies of followers is a variety with the required dimension, i.e. the vector mapping which defines this set is a local C²-diffeomorphism. The continuous differentiability of followers' strategies is critical for the existence of an interior equilibrium. Unlike the simultaneous move games, exchange can take place in one subgame while autarky can hold in another subgame, in which case only leaders (followers) make trade. Some examples buttress the approach and discuss the assumptions made on the primitives.

Suggested Citation

  • Ludovic A. Julien, 2021. "Noncooperative oligopoly equilibrium in markets with hierarchical competition," EconomiX Working Papers 2021-14, University of Paris Nanterre, EconomiX.
    • Handle: RePEc:drm:wpaper:2021-14
    as

    Download full text from publisher

    File URL: https://www.economix.fr/pdf/dt/2021/WP_EcoX_2021-14.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Colombo Luca & Labrecciosa Paola, 2008. "When Stackelberg and Cournot Equilibria Coincide," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 8(1), pages 1-7, January.
    2. Jaskold Gabszewicz, Jean & Vial, Jean-Philippe, 1972. "Oligopoly "A la cournot" in a general equilibrium analysis," Journal of Economic Theory, Elsevier, vol. 4(3), pages 381-400, June.
    3. Hanif D. Sherali, 1984. "A Multiple Leader Stackelberg Model and Analysis," Operations Research, INFORMS, vol. 32(2), pages 390-404, April.
    4. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
    5. 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.
    6. Bloch, Francis & Ghosal, Sayantan, 1997. "Stable Trading Structures in Bilateral Oligopolies," Journal of Economic Theory, Elsevier, vol. 74(2), pages 368-384, June.
    7. B. C. Eaton & Richard G. Harris (ed.), 1997. "Trade, Technology and Economics," Books, Edward Elgar Publishing, number 1020.
    8. Victor DeMiguel & Huifu Xu, 2009. "A Stochastic Multiple-Leader Stackelberg Model: Analysis, Computation, and Application," Operations Research, INFORMS, vol. 57(5), pages 1220-1235, October.
    9. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    10. Ming Hu & Masao Fukushima, 2011. "Variational Inequality Formulation of a Class of Multi-Leader-Follower Games," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 455-473, December.
    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. Balasko, Yves, 1975. "Some results on uniqueness and on stability of equilibrium in general equilibrium theory," Journal of Mathematical Economics, Elsevier, vol. 2(2), pages 95-118.
    13. 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.
    14. Julien, Ludovic A., 2017. "On noncooperative oligopoly equilibrium in the multiple leader–follower game," European Journal of Operational Research, Elsevier, vol. 256(2), pages 650-662.
    15. Birgit Grodal & Egbert Dierker, 1999. "The price normalization problem in imperfect competition and the objective of the firm," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 14(2), pages 257-284.
    16. Julien, Ludovic A., 2013. "On Stackelberg competition in strategic multilateral exchange," Research in Economics, Elsevier, vol. 67(1), pages 59-75.
    17. 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.
    18. Aghion, Philippe, 1985. "On the generic inefficiency of differentiable market games," Journal of Economic Theory, Elsevier, vol. 37(1), pages 126-146, October.
    19. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
    20. 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.
    21. 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.
    22. Jong-Shi Pang & Masao Fukushima, 2005. "Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games," Computational Management Science, Springer, vol. 2(1), pages 21-56, January.
    23. 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)

    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. Ludovic A. Julien, 2017. "Hierarchical Competition and Heterogeneous Behavior in Noncooperative Oligopoly Markets," Post-Print hal-01637298, HAL.
    2. 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.
    3. 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.
    4. 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.
    5. Ludovic A. Julien & Gagnie Pascal Yebarth, 2024. "Pareto-Optimal Taxation Mechanism in Noncooperative Strategic Bilateral Exchange," EconomiX Working Papers 2024-19, University of Paris Nanterre, EconomiX.
    6. 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.
    7. 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.
    8. Codognato, Giulio & Ghosal, Sayantan & Tonin, Simone, 2015. "Atomic Cournotian traders may be Walrasian," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 1-14.
    9. Cyrinus B. Elegbede & Ludovic A. Julien & Louis Mesnard, 2022. "On preferences and taxation mechanisms in strategic bilateral exchange," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 43-73, March.
    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. Dickson, Alex & Hartley, Roger, 2008. "The strategic Marshallian cross," Games and Economic Behavior, Elsevier, vol. 64(2), pages 514-532, November.
    12. 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.
    13. A. Dickson & R. Hartley, 2005. "The strategic Marshallian cross and bilateral oligopoly," Economics Discussion Paper Series 0523, Economics, The University of Manchester.
    14. Dmitry Levando, 2012. "A Survey Of Strategic Market Games," Economic Annals, Faculty of Economics and Business, University of Belgrade, vol. 57(194), pages 63-106, July - Se.
    15. 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.
    16. 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).
    17. Yukihiko Funaki & Harold Houba & Evgenia Motchenkova, 2020. "Market power in bilateral oligopoly markets with non-expandable infrastructures," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(2), pages 525-546, June.
    18. Régis Breton & Bertrand Gobillard, 2005. "Robustness of equilibrium price dispersion in finite market games," Post-Print halshs-00257207, HAL.
    19. Ludovic A. Julien & Fabrice Tricou, 2008. "Market Price Mechanisms and Stackelberg General Equilibria," Working Papers hal-04140726, HAL.
    20. Alex Dickson, 2013. "The Effects of Entry in Bilateral Oligopoly," Games, MDPI, vol. 4(3), pages 1-21, June.

    More about this item

    Keywords

    Pure strategies; diffeomorphisms; Stackelberg-Nash equilibrium;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

    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:drm:wpaper:2021-14. 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: Valerie Mignon (email available below). General contact details of provider: https://edirc.repec.org/data/modemfr.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.