  We consider the problem of learning optimal reserve price in repeated
auctions against non-myopic bidders, who may bid strategically in order to gain
in future rounds even if the single-round auctions are truthful. Previous
algorithms, e.g., empirical pricing, do not provide non-trivial regret rounds
in this setting in general. We introduce algorithms that obtain small regret
against non-myopic bidders either when the market is large, i.e., no bidder
appears in a constant fraction of the rounds, or when the bidders are
impatient, i.e., they discount future utility by some factor mildly bounded
away from one. Our approach carefully controls what information is revealed to
each bidder, and builds on techniques from differentially private online
learning as well as the recent line of works on jointly differentially private
algorithms.
