  We study revenue optimization learning algorithms for repeated second-price
auctions with reserve where a seller interacts with multiple strategic bidders
each of which holds a fixed private valuation for a good and seeks to maximize
his expected future cumulative discounted surplus. We propose a novel algorithm
that has strategic regret upper bound of $O(\log\log T)$ for worst-case
valuations. This pricing is based on our novel transformation that upgrades an
algorithm designed for the setup with a single buyer to the multi-buyer case.
We provide theoretical guarantees on the ability of a transformed algorithm to
learn the valuation of a strategic buyer, which has uncertainty about the
future due to the presence of rivals.
