Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Breaking Algorithmic Collusion in Human-AI Ecosystems

Natalie Collina, Eshwar Ram Arunachaleswaran, Meena Jagadeesan

TL;DR

The paper analyzes algorithmic collusion in human–AI pricing ecosystems by modeling N sellers in a repeated Bertrand game where AI agents follow equilibrium strategies and humans defect to no-regret strategies. It shows that a single human defection can dramatically reduce prices to about (ln N)/N, and that multiple defections can drive prices down further to scales like M/e^{M-1}, with tight bounds demonstrated through equal-revenue and coarse-correlated-equilibrium constructions. The authors also extend the framework to adoption-equilibria and introduce defection-aware AI agents, highlighting scenarios where collusion remains robust. This work provides a theoretical foundation explaining empirical observations of pricing dynamics in mixed human–AI markets and informs how evaluators and regulators should account for human interactions in assessing collusion risk.

Abstract

AI agents are increasingly deployed in ecosystems where they repeatedly interact not only with each other but also with humans. In this work, we study these human-AI ecosystems from a theoretical perspective, focusing on the classical framework of repeated pricing games. In our stylized model, the AI agents play equilibrium strategies, and one or more humans manually perform the pricing task instead of adopting an AI agent, thereby defecting to a no-regret strategy. Motivated by how populations of AI agents can sustain supracompetitive prices, we investigate whether high prices persist under such defections. Our main finding is that even a single human defection can destabilize collusion and drive down prices, and multiple defections push prices even closer to competitive levels. We further show how the nature of collusion changes under defection-aware AI agents. Taken together, our results characterize when algorithmic collusion is fragile--and when it persists--in mixed ecosystems of AI agents and humans.

Breaking Algorithmic Collusion in Human-AI Ecosystems

TL;DR

The paper analyzes algorithmic collusion in human–AI pricing ecosystems by modeling N sellers in a repeated Bertrand game where AI agents follow equilibrium strategies and humans defect to no-regret strategies. It shows that a single human defection can dramatically reduce prices to about (ln N)/N, and that multiple defections can drive prices down further to scales like M/e^{M-1}, with tight bounds demonstrated through equal-revenue and coarse-correlated-equilibrium constructions. The authors also extend the framework to adoption-equilibria and introduce defection-aware AI agents, highlighting scenarios where collusion remains robust. This work provides a theoretical foundation explaining empirical observations of pricing dynamics in mixed human–AI markets and informs how evaluators and regulators should account for human interactions in assessing collusion risk.

Abstract

AI agents are increasingly deployed in ecosystems where they repeatedly interact not only with each other but also with humans. In this work, we study these human-AI ecosystems from a theoretical perspective, focusing on the classical framework of repeated pricing games. In our stylized model, the AI agents play equilibrium strategies, and one or more humans manually perform the pricing task instead of adopting an AI agent, thereby defecting to a no-regret strategy. Motivated by how populations of AI agents can sustain supracompetitive prices, we investigate whether high prices persist under such defections. Our main finding is that even a single human defection can destabilize collusion and drive down prices, and multiple defections push prices even closer to competitive levels. We further show how the nature of collusion changes under defection-aware AI agents. Taken together, our results characterize when algorithmic collusion is fragile--and when it persists--in mixed ecosystems of AI agents and humans.

Paper Structure

This paper contains 53 sections, 10 theorems, 49 equations.

Table of Contents

  1. Introduction
  2. Related work
  3. Algorithmic Collusion.
  4. No-regret dynamics in pricing games.
  5. Model
  6. Repeated pricing game
  7. Repeated Game Strategies, Equilibrium, and Defections
  8. Strategies.
  9. Equilibrium concept.
  10. Defections.
  11. Market Price
  12. Market price under defections.
  13. Main Results: Defections to no-regret strategies
  14. Warmup
  15. Upper Bound: Low Market Price in Large Markets
  16. ...and 38 more sections

Key Result

Proposition 3.1

Let $N \ge 2$, $K > 1$, $T \ge 1$. Let $\mathcal{S}^{\text{simple}}$ be defined as above, and for $i \in [N]$, let $S^r_i$ be any $r(T)$-regret strategy for player $i$. Then, $\mathcal{S}^{\text{simple}}$ is an $O(1/T)$-approximate repeated game equilibrium with a market price of $\mathop{\mathrm{\t

Theorems & Definitions (23)

  • Proposition 3.1: Warm‑up
  • Proposition 3.2
  • Theorem 3.3
  • Lemma 3.4
  • Theorem 3.5
  • Theorem 3.6
  • Proposition 3.7
  • Definition 4.1
  • Theorem 4.2
  • Definition B.1: Discretized Equal Revenue Distribution (DERD) $P_{c,K}$
  • ...and 13 more