Essays in Multidimensional Mechanism Design

Abstract

This thesis analyzes three problems where a monopolistic seller is selling to an agent with multidimensional private information. While our understanding of such problems is comprehensive if the agent's private information is one-dimensional, problems with multidimensional private information are known to be ubiquitous but analytically notorious. The three chapters in this thesis make progress in understanding optimal mechanism design in such multidimensional screening problems. In the first problem, the seller is selling an object to an agent who exhibits behavioral preferences, in a departure from the standard rational models. Behavioral preferences arise because the agent is budget constrained and needs approval from a manager for outcomes beyond the budget. Such lexicographic decision-making and dierent preferences of the agent and the manager make this a two-dimensional mechanism design problem where the agent's aggregate choice shows intransitivity. We characterize the expected revenue-maximizing mechanism of the seller in this problem. In the second problem, the seller is selling a pair of goods to the agent. The agent demands two goods in a particular ratio; the bundle's valuation and the ratio are the buyer's private information. We characterize the expected revenue-maximizing mechanism of the seller in this problem. In the third model, a seller is selling an object with an inherent value and an attribute value to the agent. The value of the attribute depends on the level of the attribute, which is commonly observed by the seller and the agent, and is contractible. Since the attribute's level is not known when signing the contract, the seller can o er contingent contracts. We characterize the expected revenue-maximizing contingent contract. In particular, we show that the expected revenue-maximizing contract is deterministic under reasonable restrictions on priors.