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The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms

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Listed:
  • Simon Martin
  • Hans-Theo Normann
  • Paul Puplichhuisen
  • 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.

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  • Simon Martin & Hans-Theo Normann & Paul Puplichhuisen & Tobias Werner, 2025. "The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms," Papers 2501.07178, arXiv.org.
    • Handle: RePEc:arx:papers:2501.07178
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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. Daniel Garcia & Juha Tolvanen & Alexander K. Wagner, 2022. "Demand Estimation Using Managerial Responses to Automated Price Recommendations," Management Science, INFORMS, vol. 68(11), pages 7918-7939, November.
    3. Jeanine Miklós-Thal, 2011. "Optimal collusion under cost asymmetry," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(1), pages 99-125, January.
    4. Epivent, Andréa & Lambin, Xavier, 2024. "On algorithmic collusion and reward–punishment schemes," Economics Letters, Elsevier, vol. 237(C).
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