Revenue Optimality of Multidimensional First Price Auctions

We investigate the revenue optimality of two first-price-type auctions in the multidimensional auction setting. Namely, we focus on the multiple items, multiple bidders auction setting, involving n bidders and m items, where bidders’ valuations are additive. We let tij represent bidder i’s value for item j, belonging to type space Tij⊆ R and sampled from distribution Dij independently from all other types. We study the following mechanisms: