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Merger Incentives and Inverse Matrices from Bertrand Competition

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  • Eric Howe
  • Jingang Zhao

Abstract

This paper first inverts a general class of matrices for solving Bertrand equilibria from arbitrary coalition structures in linear Bertand oligopolies. It then studies merger incentives and obtains two main results; 1) for any asymmetric costs, mergers of any size are profitable; 2) a merger will reduce outsiders' profits when there are large cost savings or cost asymmetry. The second result is in sharp constrast to Cournot competition where mergers always increase outsiders' profits. This striking new feature not only supports the belief that Bertrand competition is more general than Cournot competition, but will also open up a new line of arguments in future attempts to block merger proposals

Suggested Citation

  • Eric Howe & Jingang Zhao, 2004. "Merger Incentives and Inverse Matrices from Bertrand Competition," Econometric Society 2004 North American Summer Meetings 586, Econometric Society.
    • Handle: RePEc:ecm:nasm04:586
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    References listed on IDEAS

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    1. Zhao, Jingang, 1991. "The Equilibria of a Multiple Object Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 171-182.
    2. Farrell, Joseph & Shapiro, Carl, 1990. "Horizontal Mergers: An Equilibrium Analysis," American Economic Review, American Economic Association, vol. 80(1), pages 107-126, March.
    3. Shapiro, Carl, 1989. "Theories of oligopoly behavior," Handbook of Industrial Organization, in: R. Schmalensee & R. Willig (ed.), Handbook of Industrial Organization, edition 1, volume 1, chapter 6, pages 329-414, Elsevier.
    4. Stephen W. Salant & Sheldon Switzer & Robert J. Reynolds, 1983. "Losses From Horizontal Merger: The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 98(2), pages 185-199.
    5. Amir, Rabah & Jin, Jim Y., 2001. "Cournot and Bertrand equilibria compared: substitutability, complementarity and concavity," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 303-317, March.
    6. Fevrier, Philippe & Linnemer, Laurent, 2004. "Idiosyncratic shocks in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 22(6), pages 835-848, June.
    7. Zhao, Jingang, 1992. "The hybrid solutions of an N-person game," Games and Economic Behavior, Elsevier, vol. 4(1), pages 145-160, January.
    8. Beth Allen, 2000. "The Future of Microeconomic Theory," Journal of Economic Perspectives, American Economic Association, vol. 14(1), pages 143-150, Winter.
    9. ZHAO, Jingang, 1991. "The equilibria of a multiple objective game," LIDAM Reprints CORE 987, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Raymond Deneckere & Carl Davidson, 1985. "Incentives to Form Coalitions with Bertrand Competition," RAND Journal of Economics, The RAND Corporation, vol. 16(4), pages 473-486, Winter.
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    Cited by:

    1. Paraskevas V. Lekeas, 2013. "Coalitional Beliefs In Cournot Oligopoly Tu Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-21.
    2. Baomin Dong & Frank Wang, 2014. "A pre-emption model of mergers," Journal of Economics, Springer, vol. 113(2), pages 187-204, October.
    3. X. Wang & Jingang Zhao, 2010. "Why are firms sometimes unwilling to reduce costs?," Journal of Economics, Springer, vol. 101(2), pages 103-124, October.
    4. Wang, X. Henry & Zhao, Jingang, 2007. "Welfare reductions from small cost reductions in differentiated oligopoly," International Journal of Industrial Organization, Elsevier, vol. 25(1), pages 173-185, February.

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    More about this item

    Keywords

    Bertrand Equilibrium; Coalition Structure; Inverse Matrix; Merger Incentives;
    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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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