A novel ex-post truthful mechanism for multi-slot sponsored search auctions

Abstract

In this paper, we advance the state-of-the-art in designing ex-post truthful multi-armed bandit (MAB) mechanisms for multi-slot sponsored search auctions (SSA) through two different contributions. First, we prove two important impossibility results which rule out the possibility of an ex-post monotone MAB allocation rule having sublinear regret with time when the click through rates (CTR) of the advertisements (ads) are affected by ad-dependent externality or position-dependent externality. The above impossibility results motivate our second contribution: when the CTRs are affected by only position-dependent externality and follow click-precedence property, we design a novel ex-post truthful mechanism for multi-slot SSAs with sublinear regret. The ex-post monotone allocation rule in the proposed mechanism non-trivially generalizes the NewCB allocation rule presented by Babaioff, Sharma, and Slivkins[2]. We derive regret bounds for this allocation rule. When a strong property such as ex-post truthfulness is required, our allocation rule performs as well as the A-VCG mechanism presented by Gatti, Lazaric, and Trovo[4] and in the special case of identical slots, our allocation rule in fact outperforms the A-VCG mechanism and has a regret of O{√T} with time.