IDEAS home Printed from https://ideas.repec.org/a/bpj/bejtec/v9y2009i1n22.html
   My bibliography  Save this article

Asymmetric Bertrand-Edgeworth Oligopoly and Mergers

Author

Listed:
  • Hirata Daisuke

    (The University of Tokyo)

Abstract

This paper investigates mixed strategy equilibria in a capacity-constrained price competition among three firms. It is shown that the equilibria in an asymmetric oligopoly are substantially different from those in a duopoly and symmetric oligopoly. In an asymmetric triopoly, it is possible that (i) a continuum of equilibria exists and that (ii) the lowest price of the smallest firm is higher than that of the others and the smallest firm earns more than the max-min profit in undominated strategies. In particular, the second finding sheds light on a new pricing incentive in Bertrand competitions. As an application, the equilibrium characterizations give rise to a new class of merger paradoxes.

Suggested Citation

  • Hirata Daisuke, 2009. "Asymmetric Bertrand-Edgeworth Oligopoly and Mergers," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 9(1), pages 1-25, July.
    • Handle: RePEc:bpj:bejtec:v:9:y:2009:i:1:n:22
    DOI: 10.2202/1935-1704.1500
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1935-1704.1500
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.2202/1935-1704.1500?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Levitan, Richard & Shubik, Martin, 1972. "Price Duopoly and Capacity Constraints," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(1), pages 111-122, February.
    2. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    3. Osborne, Martin J. & Pitchik, Carolyn, 1986. "Price competition in a capacity-constrained duopoly," Journal of Economic Theory, Elsevier, vol. 38(2), pages 238-260, April.
    4. Maskin, Eric, 1986. "The Existence of Equilibrium with Price-Setting Firms," American Economic Review, American Economic Association, vol. 76(2), pages 382-386, May.
    5. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    6. Beth Allen & Martin Hellwig, 1986. "Bertrand-Edgeworth Oligopoly in Large Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(2), pages 175-204.
    7. Hirata, Daisuke, 2008. "Bertrand-Edgeworth Equilibrium in Oligopoly," MPRA Paper 7946, University Library of Munich, Germany.
    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. De Francesco, Massimo A. & Salvadori, Neri, 2023. "Bertrand-Edgeworth game under oligopoly. General results and comparisons with duopoly," MPRA Paper 118237, University Library of Munich, Germany.
    2. Zhiqi Chen & Gang Li, 2018. "Horizontal Mergers In The Presence Of Capacity Constraints," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1346-1356, April.
    3. Tamás Balogh & Attila Tasnádi, 2012. "Does timing of decisions in a mixed duopoly matter?," Journal of Economics, Springer, vol. 106(3), pages 233-249, July.
    4. Massimo A. De Francesco & Neri Salvadori, 2022. "Bertrand–Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 803-824, July.
    5. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    6. Massimo A. De Francesco & Neri Salvadori, 2013. "Bertrand-Edgeworth Competition in an Almost Symmetric Oligopoly," Studies in Microeconomics, , vol. 1(2), pages 213-219, December.
    7. Zoltán Rácz & Attila Tasnádi, 2016. "A Bertrand–Edgeworth oligopoly with a public firm," Journal of Economics, Springer, vol. 119(3), pages 253-266, November.
    8. Massimo A. De Francesco, 2009. "A dynamic entry and price game with capacity indivisibility," Department of Economics University of Siena 577, Department of Economics, University of Siena.
    9. Victor Martínez-de-Albéniz & Kalyan Talluri, 2011. "Dynamic Price Competition with Fixed Capacities," Management Science, INFORMS, vol. 57(6), pages 1078-1093, June.
    10. Luke Garrod & Matthew Olczak, 2017. "Collusion Under Imperfect Monitoring with Asymmetric Firms," Journal of Industrial Economics, Wiley Blackwell, vol. 65(3), pages 654-682, September.
    11. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    12. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    13. Czerny, Achim I. & Zhang, Hanxiang, 2020. "Rivalry between airport ancillary and city-center supplies," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    14. Mark Armstrong & John Vickers, 2018. "Patterns of Competition with Captive Customers," Economics Series Working Papers 864, University of Oxford, Department of Economics.
    15. Massimo A. Francesco, 2014. "A Dynamic Entry And Price Game With Capacity Indivisibility," Bulletin of Economic Research, Wiley Blackwell, vol. 66(4), pages 406-419, October.
    16. Jacobs, Martin & Requate, Till, 2016. "Demand rationing in Bertrand-Edgeworth markets with fixed capacities: An experiment," Economics Working Papers 2016-03, Christian-Albrechts-University of Kiel, Department of Economics.
    17. Odenkirchen, Johannes, 2017. "Pricing Behavior of Cartel Outsiders in Incomplete Cartels," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168309, Verein für Socialpolitik / German Economic Association.
    18. De Francesco, Massimo A. & Salvadori, Neri, 2016. "Bertrand-Edgeworth games under triopoly: the equilibrium strategies when the payoffs of the two smallest firms are proportional to their capacities," MPRA Paper 69999, University Library of Munich, Germany.
    19. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    20. Garrod, Luke & Olczak, Matthew, 2018. "Explicit vs tacit collusion: The effects of firm numbers and asymmetries," International Journal of Industrial Organization, Elsevier, vol. 56(C), pages 1-25.
    21. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, 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. Roy Chowdhury, Prabal, 2008. "Bertrand-Edgeworth equilibrium with a large number of firms," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 746-761, May.
    2. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium: Manipulable residual demand," Discussion Papers 04-15, Indian Statistical Institute, Delhi.
    3. García Díaz, Antón & Kujal, Praveen, 1998. "List princing and pure strategy outcomes in a bertrand edgeworth duopoly," UC3M Working papers. Economics 6089, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Prabal Roy Chowdhury, 2004. "Bertrand-Edgeworth equilibrium with a large number of firms," Discussion Papers 04-12, Indian Statistical Institute, Delhi.
    5. Tasnádi, Attila, 2001. "A Bertrand-Edgeworth-oligopóliumok. Irodalmi áttekintés [Bertrand-Edgeworth oligopolies - a survey of the literature]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(12), pages 1081-1092.
    6. Jacobs, Martin & Requate, Till, 2016. "Bertrand-Edgeworth markets with increasing marginal costs and voluntary trading: Experimental evidence," Economics Working Papers 2016-01, Christian-Albrechts-University of Kiel, Department of Economics.
    7. Tasnadi, Attila, 2004. "Production in advance versus production to order," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 191-204, June.
    8. Tasnádi, Attila, 2020. "Production in advance versus production to order: Equilibrium and social surplus," Mathematical Social Sciences, Elsevier, vol. 106(C), pages 11-18.
    9. Pär Holmberg & Frank Wolak, 2015. "Electricity markets: Designing auctions where suppliers have uncertain costs," Cambridge Working Papers in Economics 1541, Faculty of Economics, University of Cambridge.
    10. Waddle, Roberts, 2005. "Strategic profit sharing between firms: the bertrand model," UC3M Working papers. Economics we050902, Universidad Carlos III de Madrid. Departamento de Economía.
    11. Allison, Blake A. & Lepore, Jason J., 2014. "Verifying payoff security in the mixed extension of discontinuous games," Journal of Economic Theory, Elsevier, vol. 152(C), pages 291-303.
    12. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 8634, University Library of Munich, Germany.
    13. García Díaz, Antón & Hernán González, Roberto & Kujal, Praveen, 2009. "List pricing and discounting in a Bertrand-Edgeworth duopoly," International Journal of Industrial Organization, Elsevier, vol. 27(6), pages 719-727, November.
    14. De Francesco, Massimo A. & Salvadori, Neri, 2016. "Bertrand-Edgeworth games under triopoly: the equilibrium strategies when the payoffs of the two smallest firms are proportional to their capacities," MPRA Paper 69999, University Library of Munich, Germany.
    15. Zhiqi Chen & Gang Li, 2018. "Horizontal Mergers In The Presence Of Capacity Constraints," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1346-1356, April.
    16. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    17. Jacobs, Martin & Requate, Till, 2016. "Demand rationing in Bertrand-Edgeworth markets with fixed capacities: An experiment," Economics Working Papers 2016-03, Christian-Albrechts-University of Kiel, Department of Economics.
    18. Attila Tasnádi, 2016. "Endogenous timing of moves in Bertrand–Edgeworth triopolies," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(4), pages 317-334, December.
    19. Antoniou, Fabio & Fiocco, Raffaele & Guo, Dongyu, 2017. "Asymmetric price adjustments: A supply side approach," International Journal of Industrial Organization, Elsevier, vol. 50(C), pages 335-360.
    20. Massimo A. De Francesco & Neri Salvadori, 2022. "Bertrand–Edgeworth oligopoly: Characterization of mixed strategy equilibria when some firms are large and the others are small," Metroeconomica, Wiley Blackwell, vol. 73(3), pages 803-824, July.

    More about this item

    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:bpj:bejtec:v:9:y:2009:i:1:n:22. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.