When do pricing algorithms intensify competition? A theory of online oligopoly

Abstract

Online sellers increasingly delegate pricing to rules that respond mechanically to rivals’ posted prices. This paper studies such rules in a differentiated Bertrand model in which a seller’s pricing technology is a response speed and a rule slope, and shows that rivals’ technologies enter a seller’s problem only through their product, a single induced conduct parameter measuring the total price response rivals make to a unilateral price change. Any intercept in the rule, including a fixed undercutting margin, is neutralized by optimal base pricing, so the aggressiveness that repricing software advertises has no equilibrium effect on its own. Conditional on the installed technology profile, the equilibrium posted price rises continuously in the conduct parameter, from the static Nash price under manual pricing to the joint-profit-maximizing price as symmetric matching approaches completion. The mechanism operates in the induced base-price game and requires no punishment path, no discount factor and no history dependence, which makes the boundary case an algorithmic restatement of the classical meeting-competition-clause result. The conduct representation is what the paper builds on, because it delivers comparative statics in market size, heterogeneous adoption, consumer search and entry within a single framework. Under partial adoption, non-adopters face a higher conduct parameter than adopters and price above them, while the market average price is higher under full adoption than under none; the shape of the average price in between is a numerical rather than an analytical result. Consumer search restrains prices when relative prices can move, and that restraint disappears in the full-matching limit. Free entry absorbs a substantial share of the price effect in the reported calibrations, and against a manually pricing entrant, incumbent matching makes entry easier while adoption is partial and harder as matching approaches completion. The model implies that the sign and size of the measured effect of algorithmic pricing should track market contestability and the responsiveness of rivals’ prices rather than the sophistication of the pricing algorithm, which is consistent with evidence that price effects appear in concentrated retail gasoline markets but not in the large e-commerce marketplace for which comparable evidence is available.