Three Essays In Mechanism Design

This dissertation consists of three essays in the theory of mechanism design under incomplete information. In the first essay, we analyze an implementation problem in which monetary transfers are feasible, valuations are interdependent and the set of available choices lies in a product space of lattices. This framework is general enough to subsume many interesting examples, including allocation problems with multiple objects. We identify a class of social choice rules which can be implemented in ex post equilibrium. We identify conditions under which ex post efficient social choice rules are implementable using monotone selection theory. The key conditions are extensions of the single crossing property and supermodularity. These conditions can be replaced with more tractable conditions in multiobject allocation problems with either two objects or two agents. I also show that the payments which implement monotone social decision rules coincide with the payments of (1) the classical Vickrey-Clarke-Groves mechanism with private values, and (2) the generalized Vickrey auction introduced by Ausubel [1999] in multiunit allocation problems. The second essay generalizes the analysis of optimal (revenue maximizing) mechanism design for the seller of a single object introduced by Myerson [1981]. We consider a problem in which the seller has several heterogeneous objects and buyers' valuations depend on each other's private information. We analyze two nonnested environments in which incentive constraints can be replaced with more tractable monotonicity conditions. We establish conditions under which these monotonicity conditions can be ignored, and show that several earlier analyses of the optimal mechanism design problem can be unified and generalized. In particular, problems with two complementary goods in Levin [1997] and multiunit auction problems in Maskin and Riley [1989] and Branco [1996] are special cases. The third essay considers the problem of selling internet advertising slots to advertisers. Under suitable conditions, we solve for the payments imposed by an optimal mechanism and show that it can be decentralized via prices using a linear assignment approach. At every configuration of private information, optimal mechanism can be interpreted as a menu consisting of a price for every slot.

This thesis comprises three independent essays, exploring various theoretical issues related to the design of information structures and incentive mechanisms. The first chapter investigates how to optimally design selection mechanisms, taking into account that candidates can strategically invest in the attributes upon which they are evaluated. We demonstrate that when the goal is to maximize the expected quality of admitted candidates, deterministic "pass or fail" selection rules prove to be optimal. The second chapter examines a non-Bayesian persuasion model where the receiver's belief formation process is motivated. We show that persuasion is more effective compared to the Bayesian case when it encourages the receiver to adopt a risky behavior that can lead to significant gains, but it is less effective when promoting more cautious behavior. We illustrate this finding with applications. The third and final chapter studies the distributive impacts of market segmentation. We examine how to segment a monopolistic market with a redistributive objective, i.e., favoring the poorest consumers. We show that optimal redistributive segmentations always generate Pareto-efficient allocations, but may require granting a strictly positive share of the surplus to the seller.