Learning Collusion in Episodic, Inventory-Constrained Markets

2024-10-24

arXiv.org

AI Summary

This paper investigates algorithmic tacit collusion in perishable goods markets (e.g., airline seats, hotel rooms). We model oligopolistic competition under fixed supply, finite shelf life, and dynamic inventory constraints. First, we propose the first unified framework quantifying collusion intensity by jointly characterizing competitive equilibrium and monopoly-optimal pricing. Second, we develop an efficient, closed-form-free method to compute benchmark prices, extending tacit collusion analysis—previously limited to static settings—to realistic dynamic environments with inventory and selling-horizon constraints. Third, integrating deep reinforcement learning (DRL) with game-theoretic modeling, we demonstrate that DRL agents autonomously learn and converge stably to near-monopoly pricing under complex constraints, markedly deviating from Nash equilibrium outcomes. Our results reveal structural strategic patterns underlying algorithm-driven collusion. The framework provides regulators with both theoretical tools and empirical evidence for detecting and mitigating algorithmic collusion.

Technology Category

• Game Theory and Economic Paradigms: Auctions and Market-Based Systems
• Multiagent Systems: Mechanism Design
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Pricing algorithms have demonstrated the capability to learn tacit collusion that is largely unaddressed by current regulations. Their increasing use in markets, including oligopolistic industries with a history of collusion, calls for closer examination by competition authorities. In this paper, we extend the study of tacit collusion in learning algorithms from basic pricing games to more complex markets characterized by perishable goods with fixed supply and sell-by dates, such as airline tickets, perishables, and hotel rooms. We formalize collusion within this framework and introduce a metric based on price levels under both the competitive (Nash) equilibrium and collusive (monopolistic) optimum. Since no analytical expressions for these price levels exist, we propose an efficient computational approach to derive them. Through experiments, we demonstrate that deep reinforcement learning agents can learn to collude in this more complex domain. Additionally, we analyze the underlying mechanisms and structures of the collusive strategies these agents adopt.

Problem

• Learning algorithms in collusion
• Pricing in perishable goods markets
• Deep reinforcement learning agents

Innovation

• deep reinforcement learning
• collusion metric
• perishable goods markets