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The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms (2501.07178v1)

Published 13 Jan 2025 in econ.GN, cs.AI, and q-fin.EC

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.

Summary

  • The paper demonstrates that self-learning algorithms in asymmetric Cournot duopolies generate collusive outcomes, reducing total production relative to the static Nash equilibrium.
  • The paper reveals that profit allocation aligns near the Pareto frontier, with collusive gains distributed as equal relative gains consistent with competitive reservation profits.
  • The paper indicates that increasing firm asymmetry can mitigate the severity of collusion, suggesting regulatory focus must evolve to address digital market strategies.

An Analysis of Algorithmic Collusion and Profit Distribution in Asymmetric Cournot Duopolies

The paper "The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms" explores the dynamics and outcomes of algorithmic interaction in a repeated Cournot duopoly setting, examining how algorithms collude and distribute profits in the context of asymmetric firms. The authors, Martin, Normann, Püpplichhuisen, and Werner, employ simulations using Q-learning algorithms to assess the conditions under which firms—characterized by disparate cost structures—might tacitly collude. By systematically varying the degree of asymmetry between firms while maintaining a constant Nash equilibrium outcome, this paper provides empirical insights into a domain where theoretical and experimental evidence remains sparse.

Key Findings

One of the primary takeaways from this investigation is the observation that algorithms tend to yield collusive output levels across the spectrum of firm asymmetries. Total quantities are noted to decrease relative to the static Nash equilibrium, indicating a propensity towards collusion. However, as asymmetry increases, the total quantity produced also rises, suggesting that greater asymmetry could potentially mitigate the intensity of collusion, with more output benefiting consumers—albeit not to competitive levels.

In terms of profit distribution, the paper finds that algorithm-generated solutions reside close to the Pareto frontier, with profit allocation aligning with the equal relative gains solution. This implies that profits from collusion are shared proportionally to firms' reservation profits under competitive conditions, challenging the notion that symmetric firms are inherently more collusive. Indeed, the findings suggest that asymmetric firms might engage in tacit collusion more effectively, leveraging the cost advantages of the more efficient firm.

Theoretical and Practical Implications

From a theoretical standpoint, the research supplements existing literature by validating and extending bargaining solutions to scenarios involving self-learning algorithms. It highlights the importance of considering algorithms in understanding oligopolistic behavior, as these digital agents can influence traditional economic models' predictive accuracies. The applicability of equal relative gains in algorithmic environments suggests that adaptive algorithms inherently incorporate bargaining paradigms, sharing collusive profits in a manner consistent with this established economic theory.

Practically, these results hold significant implications for competition policy and regulatory frameworks overseeing digital markets. The common presumption that symmetric markets are more susceptible to collusion might not policy implications apply when firms utilize algorithmic decision-making tools. As such, regulators may need to refine their focus to account for the distinct behavior patterns that algorithms exhibit in asymmetric markets.

Future Directions

This research opens several avenues for future studies, particularly concerning the broader application of machine learning algorithms within various oligopoly structures. There is potential to explore the interaction of algorithms with human decision-makers (hybrid systems), examining how such interactions might alter collusive dynamics. Moreover, extending the scope to include multiple firms could provide further insight into how collusion scales with market complexity.

In closing, while this paper stops short of claiming that algorithmic collusion reshapes existing paradigms, it certainly contributes valuable understanding as to how firms might leverage technology to asymmetrically coordinate behavior in ways that align with classical economic predictions. The intersection of technology and traditional economic models remains a fertile ground for advancing both theoretical insights and practical applications within modern industry contexts.

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