Title: Flawed Estimate-Then-Optimize Algorithms Drive Prices Above Competitive Levels

Abstract: This paper investigates whether straightforward algorithmic pricing mechanisms can systematically generate collusive-like pricing behaviors in markets with multiple firms. We examine entities that employ a myopic "estimate-then-optimize" strategy: each firm continuously fits a demand model based on its historical pricing and sales data, subsequently setting prices to maximize projected profits. Crucially, this demand model is misspecified because it excludes competitors' pricing strategies. We analyze the dynamic outcomes of this approach when initialized by an exploration phase involving independent, random pricing. Through a fluid-limit ordinary differential equation analysis, we identify the conditions under which this process converges to supra-competitive prices—levels higher than the Nash equilibrium. Our findings indicate that supra-competitive pricing emerges when firms initially explore within comparable price ranges on the same side of the Nash price. Furthermore, these prices can significantly exceed the Nash equilibrium; under symmetric exploration, prices may even reach monopoly levels. Simulations calibrated to a real-world multifamily rental market demonstrate that these supra-competitive outcomes are robust, persisting even when theoretical assumptions are relaxed to include finite time horizons, heterogeneous products, and nonlinear logit demand structures.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC