Horizon-Independent Optimal Pricing in Repeated Auctions with Truthful and Strategic Buyers

We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a (truthful or strategic) buyer that holds a fixed valuation. We focus on a practical situation in which the seller does not know in advance the number of played rounds (the time horizon) and has thus to use a horizon-independent pricing. First, we consider straightforward modifications of previously best known algorithms and show that these horizonindependent modifications have worser or even linear regret bounds. Second, we provide a thorough theoretical analysis of some broad families of consistent algorithms and show that there does not exist a no-regret horizon-independent algorithm in those families. Finally, we introduce a novel deterministic pricing algorithm that, on the one hand, is independent of the time horizon T and, on the other hand, has an optimal strategic regret upper bound in O(log log T ). This result closes the logarithmic gap between the previously best known upper and lower bounds on strategic regret.