Essays in Mechanism Design and Contest Theory

Citation

Goel, Sumit (2023) Essays in Mechanism Design and Contest Theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/97qy-1m35. https://resolver.caltech.edu/CaltechTHESIS:05292023-003412487

Abstract

This dissertation contains three essays. They offer contributions to the fields of mechanism design (Chapters 1 and 2) and contest theory (Chapter 3).

Chapter 1, co-authored with Wade Hann-Caruthers, studies the problem of aggregating privately-held preferences for a facility to be located on a plane. We show that for a large class of social cost functions, the mechanism that locates the facility at the coordinate-wise median of the agent’s ideal points is quantitatively optimal (in the sense that it has the smallest worst-case approximation ratio) among all deterministic, anonymous, and incentive-compatible mechanisms. We also obtain bounds on the worst-case approximation ratio of the coordinate-wise median mechanism for an important subclass of social cost functions.

Chapter 2, co-authored with Wade Hann-Caruthers, studies a principal-agent project selection problem with asymmetric information and demonstrates the value for the principal in inducing partial verifiability constraints, such as no-overselling, on the agent. We consider a setting where the principal has to choose one among a set of available projects but the relevant information, such as each project's profitability, is held by a self-interested agent who might also have its own preference over the projects. If the agent is unconstrained in its ability to manipulate its private information, the principal can do no better than randomly choosing a project. But if the agent cannot oversell any of the projects, maybe because it must support its claims with evidence, we show that a simple cutoff mechanism (agent's favorite project is chosen among those that meet a cutoff profit level and a default project) is optimal for the principal. We also find evidence in support of the well-known ally-principle which says that principal delegates more authority to an agent with more aligned preferences.

Chapter 3 studies the effect of increasing the value of prizes and competitiveness of contests on the effort exerted by participants in an incomplete information environment. We identify two natural sufficient conditions on the distribution of abilities in the population under which the interventions have opposite effects on effort. We also discuss applications to the design of optimal contests in three different environments, including the design of grading contests. Assuming that the value of a grade is determined by the information it reveals about the agent's ability, we establish a link between the informativeness of a grading scheme and the effort induced by it.

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