  We study data-driven assistants that provide congestion forecasts to users of
shared facilities (roads, cafeterias, etc.), to support coordination between
them, and increase efficiency of such collective systems. Key questions are:
(1) when and how much can (accurate) predictions help for coordination, and (2)
which assistant algorithms reach optimal predictions?
  First we lay conceptual ground for this setting where user preferences are a
priori unknown and predictions influence outcomes. Addressing (1), we establish
conditions under which self-fulfilling prophecies, i.e., "perfect"
(probabilistic) predictions of what will happen, solve the coordination problem
in the game-theoretic sense of selecting a Bayesian Nash equilibrium (BNE).
Next we prove that such prophecies exist even in large-scale settings where
only aggregated statistics about users are available. This entails a new
(nonatomic) BNE existence result. Addressing (2), we propose two assistant
algorithms that sequentially learn from users' reactions, together with
optimality/convergence guarantees. We validate one of them in a large
real-world experiment.
