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The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms

Author

Listed:
  • Simon Martin
  • Hans-Theo Normann
  • Paul Püplichhuisen
  • Tobias Werner

Abstract

We study the propensity of independent algorithms to collude in repeated Cournot duopoly games. Specifically, we investigate the predictive power of different oligopoly and bargaining solutions regarding the effect of asymmetry between firms. We find that both consumers and firms can benefit from asymmetry. Algorithms produce more competitive outcomes when firms are symmetric, but less when they are very asymmetric. Although the static Nash equilibrium underestimates the effect on total quantity and overestimates the effect on profits, it delivers surprisingly accurate predictions in terms of total welfare. The best description of our results is provided by the equal relative gains solution. In particular, we find algorithms to agree on profits that are on or close to the Pareto frontier for all degrees of asymmetry. Our results suggest that the common belief that symmetric industries are more prone to collusion may no longer hold when algorithms increasingly drive managerial decisions.

Suggested Citation

  • Simon Martin & Hans-Theo Normann & Paul Püplichhuisen & Tobias Werner, 2025. "The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms," CESifo Working Paper Series 11629, CESifo.
    • Handle: RePEc:ces:ceswps:_11629
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    References listed on IDEAS

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    1. Calvano, Emilio & Calzolari, Giacomo & Denicolò, Vincenzo & Pastorello, Sergio, 2023. "Algorithmic collusion: Genuine or spurious?," International Journal of Industrial Organization, Elsevier, vol. 90(C).
    2. Harrington, Joseph E. & Hernan Gonzalez, Roberto & Kujal, Praveen, 2016. "The relative efficacy of price announcements and express communication for collusion: Experimental findings," Journal of Economic Behavior & Organization, Elsevier, vol. 128(C), pages 251-264.
    3. Normann, Hans-Theo & Sternberg, Martin, 2023. "Human-algorithm interaction: Algorithmic pricing in hybrid laboratory markets," European Economic Review, Elsevier, vol. 152(C).
    4. Epivent, Andréa & Lambin, Xavier, 2024. "On algorithmic collusion and reward–punishment schemes," Economics Letters, Elsevier, vol. 237(C).
    5. Huelden, Tobias & Jascisens, Vitalijs & Roemheld, Lars & Werner, Tobias, 2024. "Human-machine interactions in pricing: Evidence from two large-scale field experiments," DICE Discussion Papers 412, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
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    Cited by:

    1. Hans-Theo Normann & Nina Ruli'e & Olaf Stypa & Tobias Werner, 2025. "Delegate Pricing Decisions to an Algorithm? Experimental Evidence," Papers 2510.27636, arXiv.org.

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    Keywords

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    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary 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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