Experimentation, Biased Learning, and Conjectural Variations in Competitive Dynamic Pricing

TL;DR

This paper analyzes how simple learning rules and endogenous bias from experimentation influence dynamic pricing competition, leading to convergence to conjectural variations equilibria and affecting market prices.

Contribution

It demonstrates that endogenous bias from correlated experimentation can explain convergence to conjectural variations equilibria in dynamic pricing models.

Findings

Bias from correlated experimentation can lead to supra-competitive prices.

Independent experimentation results in convergence to Nash equilibrium.

Price error decays at a rate of approximately T^{-1/2}.

Abstract

We study competitive dynamic pricing among multiple sellers, motivated by the rise of large-scale experimentation and algorithmic pricing in retail and online marketplaces. Sellers repeatedly set prices using simple learning rules and observe only their own prices and realized demand, even though demand depends on all sellers' prices and is subject to random shocks. Each seller runs two-point A/B price experiments, in the spirit of switchback-style designs, and updates a baseline price using a linear demand estimate fitted to its own data. Under certain conditions on demand, the resulting dynamics converge to a Conjectural Variations (CV) equilibrium, a classic static equilibrium notion in which each seller best responds under a conjecture that rivals' prices respond systematically to changes in its own price. Unlike standard CV models that treat conjectures as behavioral primitives, we show that these conjectures arise endogenously from the bias in demand learning induced by correlated experimentation (e.g., due to synchronized repricing schedules). This learning bias selects the long-run equilibrium, often leading to supra-competitive prices. Notably, we show that under independent experimentation, this bias vanishes and the learning dynamics converge to the standard Nash equilibrium. We provide simple sufficient conditions on demand for convergence in standard models and establish a finite-sample guarantee: up to logarithmic factors, the squared price error decays on the order of $T^{-1/2}$. Our results imply that in competitive markets, experimentation design can serve as a market design lever, selecting the equilibrium reached by practical learning algorithms.