Memoryless Algorithmic Collusion: Sure to Fail, Slow to Fall

Zhang Xu; Wei Zhao

Home/Archive/arXiv

arXiv · 2409.01147

Memoryless Algorithmic Collusion: Sure to Fail, Slow to Fall

Zhang Xu·Wei Zhao

View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper shows that, in a class of Bertrand-style competition games, memoryless Q-learning algorithms should adapt to Nash Equilibrium given sufficient explorations in the long-run. This is also verified through accelerating simulations, while the convergence time grows super-exponentially for high discount factors. The resilience of collusive outcomes in the short-run is due to exploration of unprofitable actions, making the system resemble random walk. A structural model is proposed to estimate the convergence time, which not only explains the role of discount factor, but also unveils the non-monotonic relation in learning rate, which is overlooked in the literature.

Explore related subjects

econ.TH cs.GT cs.MA

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Zhang Xu, Wei Zhao. 2026-08-09. Memoryless Algorithmic Collusion: Sure to Fail, Slow to Fall. https://arxiv.org/abs/2409.01147

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Measurement of Trustworthiness of the Online Reviews

Online review platforms shape consumer decisions, yet reported ratings and comments may be unreliable when reviewers behave inconsistently. This paper models online reviews as a sequential choice problem and proposes a formal rationality pattern function that links a reviewer's current review to their revealed preference history. Building on a two-way consistency axiom for choices from nested sets, we derive an object-specific support trajectory and an associated degree measure in [0,1] (Average Propensity to Choose a Pattern, APCP) that quantifies review trustworthiness. The measure is designed to support information updating and reduce asymmetric information by discounting reviews that are inconsistent with past behavior. A worked example illustrates how the approach assigns trustworthiness grades to reviews for different objects and how these grades can complement aggregate rating statistics. Finally, a generalized theory has been established.

econ.TH↗

arXiv2026

The Depth and Reach of Exploitation: Contracting with Endogenously Naive Consumers

Consumers can invest resources to understand and avoid their behavioral mistakes, and their incentives to do so depend on the market consequences of remaining naive. We incorporate this feedback between consumers' cognitive states and market outcomes into a general contracting model. Firms face a trade-off between the depth and reach of exploitation: deeper exploitation raises profit from a naive consumer but induces greater cognitive investment, promoting sophistication and shrinking the exploitable consumer base. This trade-off disciplines exploitation and can cause policies that benefit consumers when cognition is fixed to backfire when cognition is endogenous.

econ.TH↗

arXiv2026

Contracting under Misspecification

This paper studies agency problems when both parties worry that the model linking action to output is misspecified. With observable actions, an optimal contract is linear in output, so performance pay arises solely to share misspecification exposure, the slope reflects the parties' relative robustness concerns, and its allocation is Pareto efficient. With hidden actions, this sharing rule survives and incentives add a nonlinear correction. Misspecification concerns can polarize effort by making intermediate actions impossible to implement. Moreover, ambiguity across competing models has asymmetric effects: uncertainty about desired actions raises the principal's payoff, whereas uncertainty about deviations can lower it.

econ.TH↗