The Spoils of Algorithmic Collusion: Profit Allocation Among Asymmetric Firms

TL;DR

This paper examines how independent algorithms influence collusion in repeated Cournot duopoly games, revealing that asymmetry affects outcomes and that algorithms tend to agree on profit sharing near the Pareto frontier.

Contribution

It introduces an analysis of algorithmic collusion considering asymmetry, showing that algorithms often reach near-Pareto optimal profit allocations across asymmetries.

Findings

Algorithms produce more competitive outcomes with symmetry, less with high asymmetry.

Static Nash equilibrium underestimates total quantity, overestimates profits.

Equal relative gains solution best describes profit allocations.

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.