How Market Volatility Shapes Algorithmic Collusion: A Comparative Analysis of Learning-Based Pricing Algorithms

TL;DR

This study examines how learning-based pricing algorithms interact in duopolies under three canonical demand structures (Logit, Hotelling, Linear) and autoregressive demand shocks. By evaluating Q-Learning, PSO, Double DQN, and DDPG with two collusion metrics, it shows reinforcement-learning agents commonly sustain supra-competitive prices under stable demand, especially DDPG, and that shock regimes produce diverse effects across market structures. The findings highlight that market structure governs resilience and susceptibility to shocks, with significant policy relevance for algorithmic pricing and competition regulation. Across homogeneous and heterogeneous matchups, relative algorithm performance is largely robust to environment, though absolute outcomes vary with demand uncertainty and elasticity. The work thus informs economists, policymakers, and practitioners about potential coordination tendencies and welfare implications in automated pricing ecosystems.

Abstract

Autonomous pricing algorithms are increasingly influencing competition in digital markets; however, their behavior under realistic demand conditions remains largely unexamined. This paper offers a thorough analysis of four pricing algorithms -- Q-Learning, PSO, Double DQN, and DDPG -- across three classic duopoly models (Logit, Hotelling, Linear) and under various demand-shock regimes created by auto-regressive processes. By utilizing profit- and price-based collusion indices, we investigate how the interactions among algorithms, market structure, and stochastic demand collaboratively influence competitive outcomes. Our findings reveal that reinforcement-learning algorithms often sustain supra-competitive prices under stable demand, with DDPG demonstrating the most pronounced collusive tendencies. Demand shocks produce notably varied effects: Logit markets suffer significant performance declines, Hotelling markets remain stable, and Linear markets experience shock-induced profit inflation. Despite marked changes in absolute performance, the relative rankings of the algorithms are consistent across different environments. These results underscore the critical importance of market structure and demand uncertainty in shaping algorithmic competition, while also contributing to the evolving policy discussions surrounding autonomous pricing behavior.

Figures (3)

• Figure 1: Delta vs. RPDI Scatter Plots by Algorithm
• Figure 2: Shock Impact on Delta Across Market Structures
• Figure 3: Logit Model: Price Stability vs Shifting Benchmark