The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms

2025-01-13

AI Summary

This study investigates the emergence of spontaneous collusion and the fairness of profit allocation among asymmetric duopolists in repeated Cournot competition under algorithmic pricing. Method: We employ multi-agent reinforcement learning to simulate strategic interactions, integrating the Cournot model, Nash equilibrium analysis, and multiple bargaining solutions—including the Shapley value and Nash bargaining solution—for empirical validation. Contribution/Results: Challenging the conventional view that symmetry facilitates collusion, we demonstrate that algorithmic agents achieve near-Pareto-optimal collusive outcomes across the full spectrum of firm asymmetry. The equal relative gains solution most accurately characterizes observed behavior, outperforming classical equilibrium predictions in total welfare accuracy by a significant margin. Furthermore, moderate asymmetry—contrary to intuition—enhances consumer welfare and aggregate market output, revealing a previously overlooked efficiency benefit of structural heterogeneity in algorithmically mediated markets.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Humans and AI: Learning Human Values and Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• algorithmic collusion
• profit maximization
• fairness in profit distribution

Innovation

• Algorithmic Collusion
• Market Dynamics
• Profit Maximization