  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.
