Multi-parameter Auctions with Online Supply

We study a basic auction design problem with online supply. There are two unit-demand bidders and two types of items. The first item type will arrive first for sure, and the second item type may or may not arrive. The auctioneer has to decide the allocation of an item immediately after each item arrives, but is allowed to compute payments after knowing how many items arrived. For this problem we show that there is no deterministic truthful and individually rational mechanism that, even with unbounded computational resources, gets any finite approximation factor to the optimal social welfare. The basic multi-parameter online supply model that we study opens the space for several interesting questions about the power of randomness. There are three prominent sources of randomness. • Randomized mechanisms • Stochastic arrival • Bayesian setting (values drawn from a distribution) For each of these sources of randomness, without using the other sources of randomness, what is the optimal approximation factor one can get? The currently known best approximation factors to optimal social welfare for none of these settings is better than max{n,m} where n is the number of bidders and m is the number of items. ∗Part of the work was done when the author was at Microsoft Research. ar X iv :1 51 1. 03 69 9v 1 [ cs .G T ] 1 1 N ov 2 01 5