On Multiple Round Sponsored Search Auctions with Budgets

In a sponsored search auction the advertisement slots on a search result page are generally ordered by click-through rate. Bidders have a valuation, which is usually assumed to be linear in the click-through rate, a budget constraint, and receive at most one slot per search result page (round). We study multi-round sponsored search auctions, where the different rounds are linked through the budget constraints of the bidders and the valuation of a bidder for all rounds is the sum of the valuations for the individual rounds. All mechanisms published so far either study one-round sponsored search auctions [1, 2] or the setting where every round has only one slot and all slots have the same click-through rate, which is identical to a multi-item auction [7]. This paper contains the following three results: (1) We give the first mechanism for the multiround sponsored search problem where different slots have different click-through rates. Our mechanism is incentive compatible in expectation, individually rational in expectation, Pareto optimal in expectation, and also ex-post Pareto optimal for each realized outcome. (2) Additionally we study the combinatorial setting, where each bidder is only interested in a subset of the rounds. We give a deterministic, incentive compatible, individually rational, and Pareto optimal mechanism for the setting where all slots have the same click-through rate. (3) We present an impossibility result for auctions where bidders have diminishing marginal valuations. Specifically, we show that even for the multi-unit (one slot per round) setting there is no incentive compatible, individually rational, and Pareto optimal mechanism for private diminishing marginal valuations and public budgets. Sapienza University of Rome, Via ariosto 25, I-00185 Rome, Italy, Email: [email protected] University of Vienna, Universitätsstraße 10/9, A-1090 Vienna, Austria, Email: [email protected] Sapienza University of Rome, Via ariosto 25, I-00185 Rome, Italy, Email: [email protected] University of Vienna, Universitätsstraße 10/9, A-1090 Vienna, Austria, Email: [email protected]