Misspecified Explore-then-Exploit Leads to Supra-Competitive Prices

2026-05-15

AI Summary

This study investigates whether firms operating in a multi-firm market, when employing an exploration–exploitation pricing strategy based on a misspecified monopoly demand model that ignores competitors’ prices, systematically converge to supra-competitive prices above the Nash equilibrium. By constructing a dynamic pricing model and introducing, for the first time, a fluid-limit ordinary differential equation analysis, the authors theoretically demonstrate that under symmetric exploration, prices can spontaneously approach monopoly levels. Numerical simulations calibrated to real-world rental markets further show robustly—across finite horizons, product heterogeneity, and nonlinear Logit demand—that when firms explore within similar price ranges, equilibrium prices significantly exceed the Nash benchmark and can even approach monopoly pricing. This work thus reveals the potentially anticompetitive consequences of simple learning mechanisms in strategic interactive environments.

Abstract

We study whether simple algorithmic pricing systems can systematically produce collusive-like prices in multi-firm markets. We consider firms using an explore-then-exploit pipeline: they randomize prices during an initial exploration phase, then estimate demand from their own historical data and set prices myopically thereafter. The estimation step relies on a misspecified, monopoly-style model that omits competitors'prices. We characterize when this pipeline converges to supra-competitive prices above the Nash equilibrium, via a fluid-limit ordinary differential equation analysis. We show that supra-competitive prices arise when firms explore within similar price ranges on the same side of the Nash price. Moreover, prices can be substantially above the Nash price; we show that prices can reach monopoly levels under symmetric exploration. Simulations calibrated to a real multifamily rental market confirm that supra-competitive outcomes arise robustly beyond our theoretical assumptions, including under finite horizons, heterogeneous products, and nonlinear logit demand.

Problem

• algorithmic pricing
• misspecification
• supra-competitive prices
• explore-then-exploit
• collusion

Innovation

• misspecified demand estimation
• explore-then-exploit pricing
• supra-competitive pricing
• algorithmic collusion
• fluid-limit analysis