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Oligopoly, Complementarities, and Transformed Potentials

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  • Volker Nocke
  • Nicolas Schutz

Abstract

We adopt a potential games approach to study multiproduct-firm pricing games where products can be local complements or substitutes. We show that any such game based on an IIA demand system admits an ordinal potential, giving rise to a simple proof of equilibrium existence. We introduce the concept of transformed potential, and characterize the class of demand systems that give rise to multiproduct-firm pricing games admitting such a potential, as well as the associated transformation functions. The resulting demand systems allow for substitutability or complementarity patterns that go beyond IIA, and can resemble those induced by "one-stop shopping" behavior.

Suggested Citation

  • Volker Nocke & Nicolas Schutz, 2025. "Oligopoly, Complementarities, and Transformed Potentials," CRC TR 224 Discussion Paper Series crctr224_2025_644, University of Bonn and University of Mannheim, Germany.
    • Handle: RePEc:bon:boncrc:crctr224_2025_644
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    File URL: https://www.crctr224.de/research/discussion-papers/archive/dp644
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    References listed on IDEAS

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    3. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    4. Simon P. Anderson & Nisvan Erkal & Daniel Piccinin, 2020. "Aggregative games and oligopoly theory: short‐run and long‐run analysis," RAND Journal of Economics, RAND Corporation, vol. 51(2), pages 470-495, June.
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    More about this item

    Keywords

    Multiproduct firms; potential game; oligopoly pricing; IIA demand; complementary goods;
    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

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