Simultaneous Pooled Auctions with Multiple Bids and Preference Lists

A simultaneous pooled auction with multiple bids and preference lists is a way to auction multiple objects, in which bidders simultaneously express a bid for each object and a preference ordering over which object they would like to get in case they have the highest bid on more than one object. This type of auction has been used in the Netherlands and in Ireland to auction available spectrum. We show that this type of auction does not satisfy elementary desirable properties such as the existence of an efficient equilibrium

Draft Auctions

We introduce draft auctions, which is a sequential auction format where at each iteration players bid for the right to buy items at a fixed price. We show that draft auctions offer an exponential improvement in social welfare at equilibrium over sequential item auctions where predetermined items are auctioned at each time step. Specifically, we show that for any subadditive valuation the social welfare at equilibrium is an $O(\log^2(m))$-approximation to the optimal social welfare, where $m$ is the number of items. We also provide tighter approximation results for several subclasses. Our welfare guarantees hold for Bayes-Nash equilibria and for no-regret learning outcomes, via the smooth-mechanism framework. Of independent interest, our techniques show that in a combinatorial auction setting, efficiency guarantees of a mechanism via smoothness for a very restricted class of cardinality valuations, extend with a small degradation, to subadditive valuations, the largest complement-free class of valuations. Variants of draft auctions have been used in practice and have been experimentally shown to outperform other auctions. Our results provide a theoretical justification