| This dissertation focuses on the multidimensional exchange and allocation in various market environments. These environments include auctions, two-sided matching environments, and networks.;In the first chapter we focus on the allocation of multiple heterogeneous goods. We study a setting in which a seller possesses several, heterogeneous goods for which they have zero value. The seller wishes to design a mechanism to allocate these goods in a constrained efficient manner to buyers who face budget-constraints. This work has applications to large, government run auctions such as FCC spectrum auctions, Department of Interior oil lease auctions, or US Forest Service run timber auctions. We develop two undominated mechanisms that satisfy ex-post incentive compatibility.;The second chapter studies the problem of two-sided matching markets with complementarities. We examine many-to-one and many-to-many matching problems in which one side of the market views the other as complements. In the many-to-one case, the side of the market which can be matched with multiple agents has preferences that satisfy a particular form of complementarity called ''cardinal-complementarity." Under cardinal complementarity, an agent wished to be matched with a another only if it also is being matched by some threshold number of other players which are viewed as complements. We demonstrate that stable matchings exist in both the many-to-one and many-to-many environments under cardinal complementarity and other suitable preference restrictions. To do so, we develop two strategy-proof deferred acceptance algorithms that construct stable allocations.;Finally, we conclude by studying the problem of trading multiple, homogeneous goods in a network with intermediation. We focus on tri-partite networks, in which buyers, sellers, and intermediaries engage in multiple rounds of bilateral bargaining to facilitate the transfer of goods. We present a novel graph decomposition method that is used to partition buyers, sellers, and intermediaries into sub-types that reflect the local bargaining power they possess. We discuss an extension of the model in which the party in possession of the good may choose to sell the good to down-stream players with whom they are linked using second price auctions, rather than the benchmark bilateral bargaining protocol. |
