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Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly

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  • De Francesco, Massimo A.
  • Salvadori, Neri

Abstract

The paper extends the analysis of price competition among capacity-constrained sellers beyond the cases of duopoly and symmetric oligopoly. We first provide some general results for the oligopoly and then focus on the triopoly, providing a complete characterization of the mixed strategy equilibrium of the price game. The region of the capacity space where the equilibrium is mixed is partitioned according to the features of the mixed strategy equilibrium arising in each subregion. Then computing the mixed strategy equilibrium becomes a quite simple task. The analysis reveals features of the mixed strategy equilibrium which do not arise in the duopoly (some of them have also been discovered by Hirata (2008)).

Suggested Citation

  • 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.
    • Handle: RePEc:pra:mprapa:8634
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    References listed on IDEAS

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    1. Dan Kovenock & Raymond J. Deneckere, 1996. "Bertrand-Edgeworth duopoly with unit cost asymmetry (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(1), pages 1-25.
    2. Boccard, Nicolas & Wauthy, Xavier, 2000. "Bertrand competition and Cournot outcomes: further results," Economics Letters, Elsevier, vol. 68(3), pages 279-285, September.
    3. Simon Loertscher, 2005. "Market making oligopoly," Diskussionsschriften dp0512, Universitaet Bern, Departement Volkswirtschaft.
    4. 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.
    5. 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.
    6. Massimo A. De Francesco, 2003. "On a property of mixed strategy equilibria of the pricing game," Economics Bulletin, AccessEcon, vol. 4(30), pages 1-8.
    7. repec:ebl:ecbull:v:4:y:2003:i:30:p:1-8 is not listed on IDEAS
    8. Vives, Xavier, 1986. "Rationing rules and Bertrand-Edgeworth equilibria in large markets," Economics Letters, Elsevier, vol. 21(2), pages 113-116.
    9. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    10. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 10767, University Library of Munich, Germany, revised 26 Sep 2008.
    11. Hirata, Daisuke, 2008. "Bertrand-Edgeworth Equilibrium in Oligopoly," MPRA Paper 7946, University Library of Munich, Germany.
    12. Simon Loertscher, 2008. "Market Making Oligopoly," Journal of Industrial Economics, Wiley Blackwell, vol. 56(2), pages 263-289, June.
    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. De Francesco, Massimo A. & Salvadori, Neri, 2008. "Bertrand-Edgeworth games under oligopoly with a complete characterization for the triopoly," MPRA Paper 10767, University Library of Munich, Germany, revised 26 Sep 2008.
    6. 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.
    7. Kalyan Talluri & Victor Martínez-de-Albéniz, 2010. "Dynamic Price Competition with Fixed Capacities," Working Papers 425, Barcelona School of Economics.
    8. 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.
    9. 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.
    10. Heymann, D. & Kawamura, E. & Perazzo, R. & Zimmermann, M.G., 2014. "Behavioral heuristics and market patterns in a Bertrand–Edgeworth game," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 124-139.
    11. 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.
    12. Zoltán Rácz & Attila Tasnádi, 2016. "A Bertrand–Edgeworth oligopoly with a public firm," Journal of Economics, Springer, vol. 119(3), pages 253-266, November.
    13. 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.
    14. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    15. 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.
    16. Victor Martínez-de-Albéniz & Kalyan Talluri, 2011. "Dynamic Price Competition with Fixed Capacities," Management Science, INFORMS, vol. 57(6), pages 1078-1093, June.
    17. Kalyan Talluri & Víctor Martínez de Albéniz, 2010. "Dynamic price competition with fixed capacities," Economics Working Papers 1205, Department of Economics and Business, Universitat Pompeu Fabra.

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    2. De Francesco, Massimo A. & Salvadori, Neri, 2015. "Bertrand-Edgeworth games under triopoly: the payoffs," MPRA Paper 64638, University Library of Munich, Germany.
    3. 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.
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    20. repec:ebl:ecbull:v:4:y:2003:i:30:p:1-8 is not listed on IDEAS
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    More about this item

    Keywords

    Bertrand-Edgeworth; Price game; Oligopoly; Triopoly; Mixed strategy equilibrium;
    All these keywords.

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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