Three Essays on Mechanism Design

Citation

Song, Li (2018) Three Essays on Mechanism Design. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z91834P1. https://resolver.caltech.edu/CaltechTHESIS:09072017-153615817

Abstract

This thesis addresses mechanism design problems in three different contexts.

Chapter 2 compares two widely used student assignment mechanisms, the deferred-acceptance algorithm (DA) and the Boston algorithm (BA), in the context of the Chinese College Admission System. Two features of this system separate the study in this chapter from previous studies. First, the maximal number of schools that a student can apply to is fixed, and is significantly smaller than the total number of schools nationwide. Second, schools’ preferences over applicants are not publicly observed. Under further assumptions, which include that applicants have the same preferences over schools and schools rank applicants by a common standard, I find that students are more likely to compete for seats at top schools under DA than BA. Furthermore, there are cases in which students’ over-competition of top schools under DA results in a less efficient outcome compared to BA.

Chapter 3 studies the mechanism design problem in a market where buyers have type-dependent outside options. Previous literature usually assumes that buyers obtain a fixed value if they do not participate in a sale. This chapter focuses on scenarios in which the value of the option outside of a particular sale varies across different types of buyers. In such a scenario, an optimal mechanism for selling a private-valued item to unit-demand buyers is a second-price auction, with either a reserve price or a fixed show-up fee. This mechanism induces segregation of the market: buyers with a type which values the item high enough will exercise their outside option.

Chapter 4 analyzes grant-issuing processes in a mechanism design framework. Applicants submit their proposals for projects that may not be carried out without external funds. The grant issuer makes a selection from the proposals and decides the amount to award each selected project within a budget. This chapter characterizes optimal mechanisms to efficiently allocate the grant-issuer’s budget. The optimal mechanism overcomes the problem of mis-allocation of the current merit-based mechanism. However, the problem of crowding-out private funds still stands. This chapter also shows how the specific formof institutional constraints—the flexibility of the budget constraint, and whether an applicant can reject a grant after being rewarded — affects the form of the optimal grant-issuing mechanism.

Thesis Files