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

Fabian Raoul Pieroth, Ole Petersen and Martin Bichler

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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.

Date: 2025-10
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