  Most modern systems strive to learn from interactions with users, 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 systems balance the exploration for
learning and the competition for users. Here the users 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
systems. In our model, we consider competition between two multi-armed bandit
algorithms faced with the same bandit instance. Users arrive one by one and
choose among the two algorithms, so that each algorithm makes progress if and
only if it is chosen. We ask whether and to what extent competition
incentivizes the adoption of better bandit algorithms. We investigate this
issue for several models of user response, as we vary the degree of rationality
and competitiveness in the model. Our findings are closely related to the
"competition vs. innovation" relationship, a well-studied theme in economics.
