A vision of Two-Sided Matching Markets

Abstract

[en] In this thesis we study an implementation of auctions in assignment markets. First we lay the basis for understanding auctions of a single object with private valuations, both at first price and at second price. As a main result, we find the revenue equivalence principle concerning certain types of auction. We focus on multi-object auctions and their classes. Then, taking as a reference Shapley and Shubik (1971) [16], we explain the assignment market and its associated assignment game. We also present in detail the core and its lattice structure, as well as the buyers and the sellers optima. Finally, we put the two issues together through the writing of Demange, Gale and Sotomayor (1986) [4] - the article Multi-Item Auctions. To find the buyers-optimal core allocation we present two mechanisms. We only need the information about the valuations and the minimum price at which the seller is willing to give up the item.