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

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 expost 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 Trovò[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.