What does this research mean for the field?

Widely used online learning algorithms in repeated price competition generally converge to competitive Nash equilibrium prices, with supra-competitive pricing (collusion) occurring only under highly specific, symmetric conditions that diminish as the number of competitors increases. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.CHALLENGES_CONSENSUS.

What question did this study set out to answer?

To determine whether dynamic online learning algorithms independently converge to competitive Nash equilibria or foster tacit algorithmic collusion in repeated pricing markets.

September 2, 2026Manufacturing & Service Operations Management

Online Optimization Algorithms in Repeated Price Competition: Equilibrium Learning and Algorithmic Collusion

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Authors

JDJulius Durmann MOMatthias Oberlechner MBMartin Bichler

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Overview

Computational modeling demonstrates competitive Nash equilibrium convergence across multiarmed bandit pricing algorithms, suggesting algorithmic collusion risks in digital markets are generally...

Key Points

To determine whether dynamic online learning algorithms independently converge to competitive Nash equilibria or foster tacit algorithmic collusion in repeated pricing markets.
Conducted formal mathematical analysis of mean-based online learning algorithms interacting within repeated Bertrand price competition models.
Ran extensive numerical simulation experiments evaluating various multiarmed bandit pricing algorithms, including upper confidence bound variants, across symmetric and asymmetric seller environments with varying numbers of competitors.
Proved theoretically that mean-based online learning algorithms reliably converge to the competitive Nash equilibrium in repeated Bertrand competition.
Observed computationally that most non-mean-based bandit algorithms also converge to competitive equilibrium, with supra-competitive pricing appearing only in rare, fully symmetric implementations.
Demonstrated that supra-competitive pricing outcomes quickly decay and vanish as the number of competing sellers increases.

Cite This Study

Durmann et al. (2026) studied this question.

synapsesocial.com/papers/6a97e275c562ede874ec696a https://doi.org/10.1287/msom.2024.1389

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September 2, 2026Manufacturing & Service Operations Management

Online Optimization Algorithms in Repeated Price Competition: Equilibrium Learning and Algorithmic Collusion

View Full Paper

Ask AI

Bookmark

Authors

JDJulius Durmann MOMatthias Oberlechner MBMartin Bichler

Discussion

Member takes

Overview

Computational modeling demonstrates competitive Nash equilibrium convergence across multiarmed bandit pricing algorithms, suggesting algorithmic collusion risks in digital markets are generally...

Key Points

To determine whether dynamic online learning algorithms independently converge to competitive Nash equilibria or foster tacit algorithmic collusion in repeated pricing markets.
Conducted formal mathematical analysis of mean-based online learning algorithms interacting within repeated Bertrand price competition models.
Ran extensive numerical simulation experiments evaluating various multiarmed bandit pricing algorithms, including upper confidence bound variants, across symmetric and asymmetric seller environments with varying numbers of competitors.
Proved theoretically that mean-based online learning algorithms reliably converge to the competitive Nash equilibrium in repeated Bertrand competition.
Observed computationally that most non-mean-based bandit algorithms also converge to competitive equilibrium, with supra-competitive pricing appearing only in rare, fully symmetric implementations.
Demonstrated that supra-competitive pricing outcomes quickly decay and vanish as the number of competing sellers increases.

Cite This Study

Durmann et al. (2026) studied this question.

synapsesocial.com/papers/6a97e275c562ede874ec696a https://doi.org/10.1287/msom.2024.1389

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