Essays on college admissions and fair team formation

Victorova, Elizaveta (2022) Essays on college admissions and fair team formation. PhD thesis, University of Glasgow.

Abstract

The thesis consists of three Chapters.

The first Chapter considers college admission process with restricted applications. Each student has heuristic beliefs about the probability of being admitted and applies to a limited number of programmes within the colleges. We find that reducing the number of applications may result in an increase in total utility.

Second Chapter focuses of a team formation problem in markets with indivisible goods without transfers. Each agent is allocated equal number of goods. Since fairness notions are unattainable, we consider the relations between approximate fairness properties. We find that, contrary to general case, most approximate fairness and minimal guarantee properties are logically independent in relatively big markets. We show that when there are two agents, envy-freeness up to one good and optimality are compatible. We examine some of the well-known assignment rules and find that Round Robin and Generalised Round Robin are not efficient, although satisfy some of the approximate fairness properties. Nash Max, Utilitarian Max and Leximin procedures are efficient, but do not guarantee that any of the approximate fairness notions hold.

Third chapter investigates allocating students to equal number of elective courses. Compared to Chapter 2, here we examine many-to-many markets. We show that the Deferred Acceptance (DA) mechanism may violate the quotas, and design two modifications. We show that the modifications may allow for additional profitable manipulations compared to DA. We then simulate the allocation procedures and show that, on average, there are no more than 1% of additional profitable manipulations. When considering the number of manipulable markets, we find that roughly 20% and 18% of the markets are manipulable under our two modifications, which is low compared to the similar outcomes in one-to-many markets without lower quotas.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Colleges/Schools: College of Social Sciences > Adam Smith Business School
• Supervisor's Name: Bogomolnaia, Professor Anna, Sorokin, Dr Constantine and Moulin, Professor Herve
• Date of Award: 2022
• Depositing User: Theses Team
• Unique ID: glathesis:2022-82867
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 11 May 2022 09:34
• Last Modified: 11 May 2022 09:36
• Thesis DOI: 10.5525/gla.thesis.82867
• URI: https://theses.gla.ac.uk/id/eprint/82867