Pricing with algorithms

TL;DR

This paper analyzes how algorithms used by sellers in a repeated duopoly can sustain market power and collusion without direct communication, challenging traditional antitrust considerations.

Contribution

It introduces a model of algorithmic pricing in duopoly, showing that market power persists in equilibrium even with simple algorithms and no explicit collusion.

Findings

Monopoly outcome is the unique equilibrium in simple two-price models.

Market power persists in equilibria with multiple prices.

Expected payoffs exceed competitive outcomes, indicating collusive tendencies.

Abstract

This paper studies Markov perfect equilibria in a repeated duopoly model where sellers choose algorithms. An algorithm is a mapping from the competitor's price to own price. Once set, algorithms respond quickly. Customers arrive randomly and so do opportunities to revise the algorithm. In the simple game with two possible prices, monopoly outcome is the unique equilibrium for standard functional forms of the profit function. More generally, with multiple prices, exercise of market power is the rule -- in all equilibria, the expected payoff of both sellers is above the competitive outcome, and that of at least one seller is close to or above the monopoly outcome. Sustenance of such collusion seems outside the scope of standard antitrust laws for it does not involve any direct communication.