On consistency of optimal pricing algorithms in repeated posted-price auctions with strategic buyer

TL;DR

This paper introduces a new revenue optimization algorithm for repeated posted-price auctions with strategic buyers, achieving near-optimal regret bounds and improving upon previous algorithms through novel transformations and analysis.

Contribution

It presents a novel non-decreasing pricing algorithm with tight regret bounds, and extends strategic regret analysis to various discounting models.

Findings

Proposed algorithm has a tight $ heta(\log\log T)$ regret bound.

Improved the constant factor in the regret upper bound of PRRFES.

Extended regret analysis to geometrically concave and arbitrary discounting.

Abstract

We study revenue optimization learning algorithms for repeated posted-price auctions where a seller interacts with a single strategic buyer that holds a fixed private valuation for a good and seeks to maximize his cumulative discounted surplus. For this setting, first, we propose a novel algorithm that never decreases offered prices and has a tight strategic regret bound in $\Theta(\log\log T)$ under some mild assumptions on the buyer surplus discounting. This result closes the open research question on the existence of a no-regret horizon-independent weakly consistent pricing. The proposed algorithm is inspired by our observation that a double decrease of offered prices in a weakly consistent algorithm is enough to cause a linear regret. This motivates us to construct a novel transformation that maps a right-consistent algorithm to a weakly consistent one that never decreases offered prices. Second, we outperform the previously known strategic regret upper bound of the algorithm PRRFES, where the improvement is achieved by means of a finer constant factor $C$ of the principal term $C\log\log T$ in this upper bound. Finally, we generalize results on strategic regret previously known for geometric discounting of the buyer's surplus to discounting of other types, namely: the optimality of the pricing PRRFES to the case of geometrically concave decreasing discounting; and linear lower bound on the strategic regret of a wide range of horizon-independent weakly consistent algorithms to the case of arbitrary discounts.