Competing Bandits: The Perils of Exploration Under Competition

Most online platforms strive to learn from interactions with consumers, and many engage in exploration: making potentially suboptimal choices for the sake of acquiring new information. We initiate a study of the interplay between exploration and competition: how such platforms balance the exploration for learning and the competition for consumers. Here consumers play three distinct roles: they are customers that generate revenue, they are sources of data for learning, and they are self-interested agents which choose among the competing platforms. We consider a stylized duopoly model in which two firms face the same multi-armed bandit instance. Users arrive one by one and choose between the two firms, so that each firm makes progress on its bandit instance only if it is chosen. We study whether and to what extent competition incentivizes the adoption of better bandit algorithms, and whether it leads to welfare increases for consumers. We find that stark competition induces firms to commit to a "greedy" bandit algorithm that leads to low consumer welfare. However, we find that weakening competition by providing firms with some "free" consumers incentivizes better exploration strategies and increases consumer welfare. We investigate two channels for weakening the competition: relaxing the rationality of consumers and giving one firm a first-mover advantage. We provide a mix of theoretical results and numerical simulations. Our findings are closely related to the "competition vs. innovation" relationship, a well-studied theme in economics. They also elucidate the first-mover advantage in the digital economy by exploring the role that data can play as a barrier to entry in online markets.