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[2602.21620] Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners
Summary
This article revisits the Bertrand Paradox using a theoretical framework that incorporates no-regret learning strategies in a discrete pricing game, revealing insights into price competition dynamics.
Why It Matters
Understanding the Bertrand Paradox is crucial for economists and practitioners as it highlights discrepancies between theoretical predictions and real-world market behaviors. This study offers a fresh perspective by integrating no-regret learning, which can influence pricing strategies in competitive markets.
Key Takeaways
- The study analyzes the Bertrand pricing game with a non-increasing demand function.
- It explores how no-regret learners can lead to high-price outcomes contrary to classical predictions.
- The research provides experimental support for theoretical findings on no-swap regret learners.
- Insights from this study can inform pricing strategies in competitive markets.
- The paper contributes to the understanding of game theory and machine learning intersections.
Computer Science > Computer Science and Game Theory arXiv:2602.21620 (cs) [Submitted on 25 Feb 2026] Title:Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners Authors:Arnab Maiti, Junyan Liu, Kevin Jamieson, Lillian J. Ratliff View a PDF of the paper titled Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners, by Arnab Maiti and 3 other authors View PDF HTML (experimental) Abstract:We study the discrete Bertrand pricing game with a non-increasing demand function. The game has $n \ge 2$ players who simultaneously choose prices from the set $\{1/k, 2/k, \ldots, 1\}$, where $k\in\mathbb{N}$. The player who sets the lowest price captures the entire demand; if multiple players tie for the lowest price, they split the demand equally. We study the Bertrand paradox, where classical theory predicts low prices, yet real markets often sustain high prices. To understand this gap, we analyze a repeated-game model in which firms set prices using no-regret learners. Our goal is to characterize the equilibrium outcomes that can arise under different no-regret learning guarantees. We are particularly interested in questions such as whether no-external-regret learners can converge to undesirable high-price outcomes, and how stronger guarantees such as no-swap regret shape the emergence of competitive low-price behavior. We address these and related questions through a theoretical analysis, complemented by experiments that support the theo...
