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Oligopoly, Complementarities, and Transformed Potentials

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  • Volker Nocke

  • Nicolas Schutz

Abstract

We develop a potential games approach to study multiproduct-firm pricing games.We introduce the new concept of transformed potential and characterize the classes of demand systems that give rise to pricing games admitting such a potential. The resulting demand systems may contain nests (of closer substitutes) or baskets (of products that are purchased jointly), or combinations thereof. These demand systems allow for flexible substitution patterns, and can feature product complementarities arising from joint purchases and substitution away from the outside option. Combining the potential games approach with a competition-in-utility approach, we derive powerful results on existence of pure-strategy Nash equilibria.

Suggested Citation

  • Volker Nocke & Nicolas Schutz, 2025. "Oligopoly, Complementarities, and Transformed Potentials," CRC TR 224 Discussion Paper Series crctr224_2025_644_v3, University of Bonn and University of Mannheim, Germany, revised Apr 2026.
    • Handle: RePEc:bon:boncrc:crctr224_2025_644_v3
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    References listed on IDEAS

    as
    1. Konrad Stahl, 1982. "Location and Spatial Pricing Theory with Nonconvex Transportation Cost Schedules," Bell Journal of Economics, The RAND Corporation, vol. 13(2), pages 575-582, Autumn.
    2. Guillermo Gallego & Ruxian Wang, 2014. "Multiproduct Price Optimization and Competition Under the Nested Logit Model with Product-Differentiated Price Sensitivities," Operations Research, INFORMS, vol. 62(2), pages 450-461, April.
    3. Daniel Ershov & Jean‐William Laliberté & Mathieu Marcoux & Scott Orr, 2025. "Estimating Complementarity With Large Choice Sets: An Application to Mergers," RAND Journal of Economics, RAND Corporation, vol. 56(4), pages 689-707, December.
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    Keywords

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    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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