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Price vs quantity in duopoly supergames with close substitutes

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  • Svend Albæk
  • Luca Lambertini

Abstract

We model the non-cooperative choice between quantity and price in order to stabilize collusion, through two meta-games where each firm alternatively considers its payoff in the market supergame as directly related to its own or the rival's ability to collude. In the first setting, (i) if cartel profits are evenly split, firms collude in prices irrespective of the degree of differentiation, so that initially a Prisoners' Dilemma is observed, while for very close substitutes the outcome is Pareto-eficient; (ii) if Nash bargaining is adopted, price setting is dominant when substitutability is low, while no dominant strategy exists when substitutability is high, and the game has two asymmetric equilibria. In the second setting, the Nash equilibrium is unique and Pareto-eficient for the most part of the substitutability range, while again two asymmetric equilibria obtain when products are very close substitutes.
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Suggested Citation

  • Svend Albæk & Luca Lambertini, 2004. "Price vs quantity in duopoly supergames with close substitutes," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 38(4), pages 567-577, December.
    • Handle: RePEc:spr:anresc:v:38:y:2004:i:4:p:567-577
    DOI: 10.1007/s00168-003-0182-5
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    References listed on IDEAS

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    1. Hamilton, Jonathan H. & Slutsky, Steven M., 1990. "Endogenous timing in duopoly games: Stackelberg or cournot equilibria," Games and Economic Behavior, Elsevier, vol. 2(1), pages 29-46, March.
    2. Abreu, Dilip & Pearce, David & Stacchetti, Ennio, 1986. "Optimal cartel equilibria with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 39(1), pages 251-269, June.
    3. Abreu, Dilip, 1986. "Extremal equilibria of oligopolistic supergames," Journal of Economic Theory, Elsevier, vol. 39(1), pages 191-225, June.
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    Cited by:

    1. Stefano Colombo, 2016. "Mixed oligopolies and collusion," Journal of Economics, Springer, vol. 118(2), pages 167-184, June.
    2. Baldelli, Serena & Lambertini, Luca, 2006. "Price vs quantity in a duopoly supergame with Nash punishments," Research in Economics, Elsevier, vol. 60(3), pages 121-130, September.
    3. L. Lambertini & S. Poddar & D. Sasaki, 1998. "Price versus Quantity Competition with Cost Sharing," Working Papers 343, Dipartimento Scienze Economiche, Universita' di Bologna.
    4. Delbono, Flavio & Lambertini, Luca, 2020. "On the collusive nature of managerial contracts based on comparative performance," Research in Economics, Elsevier, vol. 74(1), pages 12-18.
    5. Leonard F. S. Wang & Han Wang, 2021. "Will managerial delegation impede upstream collusion?," Journal of Economics, Springer, vol. 134(2), pages 127-146, October.

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    More about this item

    Keywords

    C72; D43; L13;
    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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