Algorithmic Collusion Without Threats (2409.03956v2)

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 ofalgorithmic collusion'' may need to be expanded, to include strategies without explicitly encoded threats.

• The paper demonstrates that no-regret algorithms paired with static strategies can yield near-monopoly prices, securing a significant share of monopoly revenue.
• It employs the Bertrand duopoly and Multinomial-logit models to quantify how implicit algorithmic interactions elevate prices without explicit collusion.
• The findings suggest that regulators must reconsider traditional approaches, as rational algorithmic behavior can inadvertently foster anti-competitive pricing.

Algorithmic Collusion Without Threats

The paper "Algorithmic Collusion Without Threats" by Eshwar Ram Arunachaleswaran et al. addresses the emergence of supra-competitive prices in automated pricing environments devoid of explicit threats. It challenges the conventional economic belief that explicit threats or failure to optimize govern the emergence of high prices, proposing that merely deploying no-regret algorithms can lead to such outcomes.

Core Investigations

The authors structure their investigation around two primary models of competition: the Bertrand Duopoly model and the Multinomial-logit model. Both models are employed to explore the dynamics between two sellers who repeatedly interact in a market, adjusting their pricing strategies either via no-regret algorithms or other heuristic approaches.

Bertrand Duopoly Model

In the Bertrand model, where the seller with the lower price captures the entire demand, the paper establishes that Nash Equilibria lead to competitive prices near production cost. However, in a Stackelberg setting (where one seller commits to a strategy first), supra-competitive prices can emerge. This foundational result underpins the observations in the more complex settings of repeated interactions.

Key Results

1. Static Strategies & No-Regret Learning: The paper demonstrates that when one player (the learner) employs any no-regret algorithm and the other (the optimizer) adopts a static pricing strategy, both can achieve near monopoly prices. Specifically, the optimizer can ensure a significant fraction of the monopoly revenue ($\Omega(1)$) by merely choosing static, non-responsive strategies. This robust result holds even when the learner uses any no-regret algorithm, emphasizing that optimization success isn't contingent on dynamic threat-based strategies.
2. Implications for Pricing Dynamics: It follows that the resulting supra-competitive prices arise naturally from the structure of no-regret learning. Both sellers benefit from these high prices, splitting the monopoly-like profits, which ensures that neither has an incentive to deviate significantly. This finding notably extends to a Nash equilibrium context in algorithm space: pairs of strategies involving no-regret algorithms and static strategies can stabilize at high prices without explicit threats.
3. Algorithmic Equilibria Insights: The research highlights the nuance that deploying a no-swap regret algorithm still leaves room for tuned static responses by competitors, systematically yielding higher than competitive prices. This contradicts traditional economic perspectives, suggesting that prevention of explicit threats isn't sufficient to guarantee competitive pricing.

Practical and Theoretical Implications

The implications of these results are profound for both theoretical understanding and practical regulation of automated pricing strategies.

• Theoretical Insight:

The paper shifts the dialogue on collusion in algorithmic settings by illustrating that natural market dynamics, even with well-behaved, rational algorithms, can lead to high prices. This divergence from traditional economic theories necessitates a reconsideration of what constitutes collusive behavior in algorithmic markets.

• Regulatory Considerations:

Practically, this suggests that merely banning threat-based strategies might be insufficient. Regulators may need to scrutinize the deployment and interaction of even ostensibly benign no-regret algorithms. There is a need to expand the definition of anti-competitive behavior to encapsulate these algorithmic nuances.

Speculations on Future Developments

Given the robust implications of these findings, future developments in AI and algorithmic market interactions may include:

• Enhanced Regulatory Frameworks:

Regulations could evolve to more nuanced definitions of collusive behavior, potentially incorporating the underlying algorithmic frameworks and their interaction dynamics.

• Algorithmic Intervention Designs:

New frameworks or algorithms could be developed to specifically counteract the implicit collusion that emerges from combined no-regret learning strategies. This might include creating mechanisms to enforce more competitive outcomes dynamically.

• Interdisciplinary Research:

Further research involving both economic theories and computational algorithm design could yield deeper insights into mitigating supra-competitive pricing while maintaining market efficiencies.

Conclusion

The paper provides a compelling exploration of algorithmic collusion, extending beyond explicit threat-based strategies to encompass interactions governed purely by no-regret algorithms. It bridges a critical gap in understanding how contemporary learning algorithms can naturally lead to anti-competitive outcomes, prompting a reevaluation of both theoretical frameworks and practical regulatory approaches in algorithmic pricing.