Algorithmic Collusion Without Threats
Eshwar Ram Arunachaleswaran, Natalie Collina, Sampath Kannan, Aaron Roth, Juba Ziani
TL;DR
The paper addresses whether pricing algorithms can induce collusive, supra-competitive prices without explicit threats. It demonstrates that when a leader uses any no-regret algorithm and a follower optimizer responds within the induced environment, near-monopoly prices arise in both Bertrand and multinomial-logit models, and that there exist Nash equilibria in algorithm space without threats. Notably, supra-competitive outcomes can emerge even when the follower employs non-responsive or static policies, and these results extend to common learning dynamics such as mean-based no-regret, which may converge to competitive prices only when both sellers fully use certain dynamics. Collectively, the work suggests that algorithmic collusion need not rely on explicit punishments, challenging traditional anti-collusion intuitions and informing regulatory perspectives on pricing algorithms.
Abstract
There has been substantial recent concern that pricing algorithms might learn to ``collude.'' Supra-competitive prices can emerge as a Nash equilibrium of repeated pricing games, in which sellers play strategies which threaten to punish their competitors who refuse to support high prices, and these strategies can be automatically learned. In fact, a standard economic intuition is that supra-competitive prices emerge from either the use of threats, or a failure of one party to optimize their payoff. Is this intuition correct? Would preventing threats in algorithmic decision-making prevent supra-competitive prices when sellers are optimizing for their own revenue? No. We show that supra-competitive prices can emerge even when both players are using algorithms which do not encode threats, and which optimize for their own revenue. We study sequential pricing games in which a first mover deploys an algorithm and then a second mover optimizes within the resulting environment. We show that if the first mover deploys any algorithm with a no-regret guarantee, and then the second mover even approximately optimizes within this now static environment, monopoly-like prices arise. The result holds for any no-regret learning algorithm deployed by the first mover and for any pricing policy of the second mover that obtains them profit at least as high as a random pricing would -- and hence the result applies even when the second mover is optimizing only within a space of non-responsive pricing distributions which are incapable of encoding threats. In fact, there exists a set of strategies, neither of which explicitly encode threats that form a Nash equilibrium of the simultaneous pricing game in algorithm space, and lead to near monopoly prices. This suggests that the definition of ``algorithmic collusion'' may need to be expanded, to include strategies without explicitly encoded threats.