Data‐driven collusion and competition in a pricing duopoly with multinomial logit demand

Abstract

We consider dynamic pricing and demand learning in a duopoly with multinomial logit demand, both from the perspective where firms compete against each other and from the perspective where firms aim to collude to increase revenues. We show that joint‐revenue maximization is not always beneficial to both firms compared to the Nash equilibrium, and show that several other axiomatic notions of collusion can be constructed that are always beneficial to both firms and a threat to consumer welfare. Next, we construct a price algorithm and prove that it learns to charge supra‐competitive prices if deployed by both firms, and learns to respond optimally against a class of competitive algorithms. Our algorithm includes a mechanism to infer demand observations from the competitor's price path, so that our algorithm can operate in a setting where prices are public but demand is private information. Our work contributes to the understanding of well‐performing price policies in a competitive multi‐agent setting, and shows that collusion by algorithms is possible and deserves the attention of lawmakers and competition policy regulators.