The Illusion of Collusion

Abstract

Algorithmic agents are used in a variety of competitive decision-making settings, including pricing contexts that range from online retail to residential home rental. We study the emergence of algorithmic collusion when competing agents employ multi-armed bandit algorithms and competition is modeled as a repeated Prisoner's Dilemma game. Notably, agents in our setting perform online learning with no prior model of game structure and have no direct knowledge of competitor states or actions, thus they cannot learn strategies that depend on these factors. These context-free bandits nonetheless frequently learn seemingly collusive behavior, a phenomenon we term naive collusion. Our results reveal that whether naive collusion emerges depends starkly on the choice of behavior policy employed by bandit learners. The mechanism underpinning the emergence of collusive outcomes is synchronicity in agent action plays, where synchronicity captures how often agents play the same action. We show that in the long-run, naive algorithmic collusion never emerges when both agents use a broad class of persistently random algorithms, including the epsilon-greedy algorithm without epsilon decay, sometimes emerges when both agents use greedy-in-the-limit algorithms which feature randomness during exploration but are asymptotically deterministic, and always emerges when both agents use deterministic bandit learning algorithms like those in the well-known upper confidence bound (UCB) family. We highlight market and algorithmic conditions under which one can and cannot predict a priori whether collusion will occur. Our findings have several policy implications: preventing pricing algorithms from conditioning their actions on competitor prices may not preclude algorithmic collusion, symmetry in algorithms may increase collusion potential, and the emergence of algorithmic collusion is path dependent.