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Price Strategy Oligopoly With Product Variation


  • Lloyd Shapley
  • Martin Shubik


This article presents a mathematical model for monopolistic price competition among firms with differentiated products. The conditions which distinguish the Chamberlinian analysis from that of Edgeworth are examined. Product differentiation is not sufficient to guarantee the existence of a stable non‐cooperative equilibrium point in terms of price. The relationship among the degree of product variation, amount of capacity, and stability are examined. Explicit formulas are obtained for the non‐cooperative equilibrium and the capacity conditions for its existence. The behavior of the model as the degree of differentiation approaches zero and as competition becomes large is examined. This connects the analysis of oligopoly with the analysis of pure competition.

Suggested Citation

  • Lloyd Shapley & Martin Shubik, 1969. "Price Strategy Oligopoly With Product Variation," Kyklos, Wiley Blackwell, vol. 22(1), pages 30-44, February.
  • Handle: RePEc:bla:kyklos:v:22:y:1969:i:1:p:30-44
    DOI: 10.1111/j.1467-6435.1969.tb02520.x

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    Cited by:

    1. Martin Shubik, 1975. "On the Role of Numbers and Information in Competition," Revue Économique, Programme National Persée, vol. 26(4), pages 605-621.
    2. Symeonidis, George, 2018. "Collusion, profitability and welfare: Theory and evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 145(C), pages 530-545.
    3. Bos, Iwan & Vermeulen, Dries, 2021. "On pure-strategy Nash equilibria in price–quantity games," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    4. Choné, Philippe & Linnemer, Laurent, 2020. "Linear demand systems for differentiated goods: Overview and user’s guide," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    5. Xavier Vives, 2008. "Innovation And Competitive Pressure," Journal of Industrial Economics, Wiley Blackwell, vol. 56(3), pages 419-469, December.
    6. Mongoljin Batsaikhan & Norovsambuu Tumennasan, 2018. "Output Decisions and Price Matching: Theory and Experiment," Management Science, INFORMS, vol. 64(8), pages 3609-3624, August.
    7. Xavier Wauthy & Nicolas Boccard, 2005. "Equilibrium payoffs in a Bertrand-Edgeworth model with product differentiation," Economics Bulletin, AccessEcon, vol. 12(11), pages 1-8.
    8. Farm, Ante, 2009. "Market Sharing and Price Leadership," Working Paper Series 3/2009, Stockholm University, Swedish Institute for Social Research.
    9. Philippe Choné & Laurent Linnemer, 2019. "The quasilinear quadratic utility model: an overview," CESifo Working Paper Series 7640, CESifo.
    10. Albaek, Svend & Overgaard, Per Baltzer, 1998. "Receiver discretion in signalling models: Information transmission to competing retailers," International Journal of Industrial Organization, Elsevier, vol. 16(2), pages 209-228, March.
    11. repec:ebl:ecbull:v:12:y:2005:i:11:p:1-8 is not listed on IDEAS
    12. Daniel Greenfield & Jeremy A. Sandford, 2021. "Upward pricing pressure in mergers of capacity‐constrained firms," Economic Inquiry, Western Economic Association International, vol. 59(4), pages 1723-1747, October.
    13. Frederick Dongchuhl Oh & Junghum Park, 2019. "Potential competition and quality disclosure," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 28(4), pages 614-630, November.
    14. Zhou, Yuan & Xie, Jinxing, 2014. "Potentially self-defeating: Group buying in a two-tier supply chain," Omega, Elsevier, vol. 49(C), pages 42-52.
    15. Quint, Daniel, 2014. "Imperfect competition with complements and substitutes," Journal of Economic Theory, Elsevier, vol. 152(C), pages 266-290.

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