Möller, Markus
(2022).
Essays on Matching Markets.
PhD thesis, Universität zu Köln.
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Abstract
The thesis consists of three chapters in the theory of matching markets. In Chapter 2, I study a central authority's ability to commit to a publicly announced mechanism in a one-to-one agent-object matching model. The authority announces a strategy-proof mechanism and then privately selects a mechanism to initiate a matching. An agent's observation in form of the final matching has an innocent explanation (Akbarpour and Li, 2020), if given the agent's reported preferences, there is a combination with other agents' preferences leading to an identical observation under the announced mechanism. The authority can only commit up to safe deviations (Akbarpour and Li, 2020)---mechanisms that produce only observations with innocent explanations. For efficient or stable announcements, I show that no safe deviation exists if and only if the announced mechanism is dictatorial. I establish that the Deferred Acceptance (DA) Mechanism (Gale and Shapley, 1962) implies commitment to stability. Moreover, group strategy-proof and efficient announcements allow commitment to efficiency only if they are dictatorial. In Chapter 3, we study The Efficiency Adjusted Deferred Acceptance Matching Rule (EDA) which is a promising candidate mechanism for public school assignment. A potential drawback of EDA is that it could encourage students to game the system since it is not strategy-proof. However, to successfully strategize, students typically need information that is unlikely to be available to them in practice. We model school choice under incomplete information and show that EDA is regret-free truth-telling, which is a weaker incentive property than strategy-proofness and was introduced by (Fernandez, 2020). We also show that there is no efficient matching rule that weakly Pareto dominates a stable matching rule and is regret-free truth-telling. Note that without modifications the EDA as introduced by (Kesten, 2010) weakly Pareto dominates a stable matching rule, but it is not efficient. In Chapter 4, I study agents’ incentives in a one-to-one object allocation model where agents are envious. Among all agents whose assignment is tracked by some agent, the agent envies those who are matched to an object she prefers to her own assignment. Given a mechanism and agents’ actions, agent i’s envy towards agent j at object x under the induced matching is inevitable if i has no action where she does not envy j at x, given one keeps the actions of other agents unchanged. A matching mechanism is envyproof, if for each market and agent, any envy under truthful revelation of preferences is inevitable. Envy-proofness is a concept that is stronger than strategy-proofness. I show that the Top Trading Cycle (TTC) Mechanism is envy-proof. Moreover, the unique strategy-proof and stable mechanism, the Deferred Acceptance Mechanism, is not envy-proof.
| Item Type: | Thesis (PhD thesis) | ||||||||
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| URN: | urn:nbn:de:hbz:38-629384 | ||||||||
| Date: | 30 August 2022 | ||||||||
| Language: | English | ||||||||
| Faculty: | Faculty of Management, Economy and Social Sciences | ||||||||
| Divisions: | Faculty of Management, Economics and Social Sciences > Economics > Microeconomics, Institutions and markets > Professorship 2 for Economics Behavior und Design | ||||||||
| Subjects: | Economics | ||||||||
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| Date of oral exam: | 7 July 2022 | ||||||||
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/62938 |
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