Algorithmic Predation: Equilibrium Analysis in Dynamic Oligopolies with Smooth Market Sharing

2025-10-30

AI Summary

The existence and structure of equilibrium strategies in dynamic oligopolies with firm exit—particularly in models permitting predatory pricing—have remained long-standing open questions. Method: This paper pioneers the application of deep reinforcement learning (DRL) to compute subgame-perfect equilibria in finite-horizon, asymmetric-cost oligopoly models featuring endogenous exit, under both complete and incomplete information. Contribution/Results: Theory-guided DRL training converges stably to equilibrium policies. Crucially, firms with cost advantages rationally employ predatory pricing as a credible entry-deterrence strategy, constituting a valid equilibrium behavior. These findings provide novel computational evidence for the strategic rationality of predatory pricing, overcome classical game-theoretic limitations in high-dimensional dynamic settings, and deliver a tractable, simulation-based framework for antitrust policy evaluation.

Technology Category

• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search
• Machine Learning: Reinforcement Learning

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Predatory pricing -- where a firm strategically lowers prices to undermine competitors -- is a contentious topic in dynamic oligopoly theory, with scholars debating practical relevance and the existence of predatory equilibria. Although finite-horizon dynamic models have long been proposed to capture the strategic intertemporal incentives of oligopolists, the existence and form of equilibrium strategies in settings that allow for firm exit (drop-outs following loss-making periods) have remained an open question. We focus on the seminal dynamic oligopoly model by Selten (1965) that introduces the subgame perfect equilibrium and analyzes smooth market sharing. Equilibrium can be derived analytically in models that do not allow for dropouts, but not in models that can lead to predatory pricing. In this paper, we leverage recent advances in deep reinforcement learning to compute and verify equilibria in finite-horizon dynamic oligopoly games. Our experiments reveal two key findings: first, state-of-the-art deep reinforcement learning algorithms reliably converge to equilibrium in both perfect- and imperfect-information oligopoly models; second, when firms face asymmetric cost structures, the resulting equilibria exhibit predatory pricing behavior. These results demonstrate that predatory pricing can emerge as a rational equilibrium strategy across a broad variety of model settings. By providing equilibrium analysis of finite-horizon dynamic oligopoly models with drop-outs, our study answers a decade-old question and offers new insights for competition authorities and regulators.

Problem

• Analyzing predatory pricing equilibria in dynamic oligopolies
• Computing equilibria in finite-horizon games with firm exit
• Verifying predatory pricing as rational equilibrium strategy

Innovation

• Using deep reinforcement learning for equilibrium computation
• Analyzing dynamic oligopoly models with firm drop-outs
• Verifying predatory pricing as rational equilibrium strategy