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

arXiv: https://arxiv.org/abs/2510.27008 · HTML: https://mlsanity.com/paper/2510.27008/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Adversarial robustness and RL in finance, one of 15 directions in Deep reinforcement learning methods.
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Placed in

- Deep reinforcement learning methods / [Adversarial robustness and RL in finance](https://mlsanity.com/deeprl/adversarial-robustness-and-rl-in-finance/)

## Builds on (most cited first, 6 of 6)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Policy-Gradient Algorithms Have No Guarantees of Convergence in Linear Quadratic Games](https://mlsanity.com/paper/1907.03712/) (2019)
- [Dynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference](https://mlsanity.com/paper/1804.03219/) (2018)
- [On the Convergence of Learning Algorithms in Bayesian Auction Games](https://mlsanity.com/paper/2311.15398/) (2023)
- [Algorithmic Pricing and Algorithmic Collusion](https://mlsanity.com/paper/2504.16592/) (2025)
- [On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions](https://mlsanity.com/paper/2401.01185/) (2024)

## Abstract (arXiv)

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.