  We consider the problem of repeatedly auctioning a single item to multiple
i.i.d buyers who each use a no-regret learning algorithm to bid over time. In
particular, we study the seller's optimal revenue, if they know that the buyers
are no-regret learners (but only that their behavior satisfies some no-regret
property -- they do not know the precise algorithm/heuristic used).
  Our main result designs an auction that extracts revenue equal to the full
expected welfare whenever the buyers are "mean-based" (a property satisfied by
standard no-regret learning algorithms such as Multiplicative Weights,
Follow-the-Perturbed-Leader, etc.). This extends a main result of [BMSW18]
which held only for a single buyer.
  Our other results consider the case when buyers are mean-based but never
overbid. On this front, [BMSW18] provides a simple LP formulation for the
revenue-maximizing auction for a single-buyer. We identify several formal
barriers to extending this approach to multiple buyers.
