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Asymmetric Bertrand-Edgeworth Oligopoly and Mergers

Author

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  • Hirata Daisuke

    (The University of Tokyo, dhirata@fas.harvard.edu)

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
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    References listed on IDEAS

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    Citations

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    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. 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.
    3. Mark Armstrong & John Vickers, 2022. "Patterns of Competitive Interaction," Econometrica, Econometric Society, vol. 90(1), pages 153-191, January.
    4. 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.
    5. Zoltán Rácz & Attila Tasnádi, 2016. "A Bertrand–Edgeworth oligopoly with a public firm," Journal of Economics, Springer, vol. 119(3), pages 253-266, November.
    6. 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.
    7. Victor Martínez-de-Albéniz & Kalyan Talluri, 2011. "Dynamic Price Competition with Fixed Capacities," Management Science, INFORMS, vol. 57(6), pages 1078-1093, June.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    12. Armstrong, Mark & Vickers, John, 2018. "Patterns of Competition with Captive Customers," MPRA Paper 90362, University Library of Munich, Germany.
    13. 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.
    14. 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.
    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. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.

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