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

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.