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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, the algorithms respond quickly. Customers arrive randomly and
sellers can periodically revise their algorithms. The main results are that (i) for the
simple two-price model with standard profit functions, monopoly pricing is the unique
equilibrium outcome, and (ii) for any general finite price grid, all equilibrium outcomes
feature supra-competitive pricing. Sustenance of such collusion seems outside the scope
of current antitrust laws for it does not involve any direct communication.
