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Title:Three essays on matching over characteristics
Author(s):Sahajdack, Thomas Clay
Director of Research:Williams, Steven R
Doctoral Committee Chair(s):Williams, Steven R
Doctoral Committee Member(s):Bernhardt, Dan; Miller, Nolan; Deltas, George
Department / Program:Economics
Degree Granting Institution:University of Illinois at Urbana-Champaign
market design
Abstract:This thesis is divided into three chapters. In the first chapter, I study the use of an alternative method of eliciting preferences in a two-sided, one-to-one matching market. In the second chapter, I analyze this method of eliciting preferences in a two-sided, many-to-one matching setting with different primitives on preferences. Finally, in the third chapter, I use survey data to estimate the effects of information exposure on the reported preferences of the participants with the alternative method of eliciting preferences. Many two-sided matching markets, in practice, are large, complex for the participants and suffer from incomplete information. These features provide challenges for matching theorists, and these challenges are not always well met with traditional matching mechanisms where agents directly submit a ranking of agents on the other side of the market. In Chapter 1, I study one approach to dealing with these challenges that, while used in some real world matching markets, has not received much attention in the literature. I analyze an alternative message space where agents submit some combination of their own characteristics and their preferences over characteristics of other participants instead of directly submitting preference rankings. By doing this, the market designer can elicit preferences without requiring agents to rank each other directly, which is often infeasible in real world applications. Using online dating markets as a motivating example, I study the incentive, mechanism and market design implications of using the alternative message space approach in one-to-one matching markets. I find that for a restricted class of preference rankings, using this approach can decrease the number of binary pieces of information, such as either/or questions, necessary to generate the preference rankings of agents. I quantify a lower bound on the number of such questions that allows for any agent to have his or her true preference ranking generated based on his or her answers. I show that a strategy-proof matching algorithm under direct reporting of preference rankings can extend strategy-proofness into the alternative message space if that message space only asks for either an agent's own characteristics or their desired traits in a partner. I also show how an alternative message space that asks an agent for both aspects can lead to dishonesty, even when used with well-known strategy-proof matching algorithms under direct reporting of preference rankings such as deferred acceptance for the proposing side. I identify the optimal strategy of an agent when the message space cannot generate their true preferences but the mechanism is strategy-proof and discuss the limitations of such a strategy in practice. In the Chapter 2, I shift the focus on understanding the implications of the alternative message space to a two-sided, many-to-one matching market such as centralized public school choice. I also change the primitive of the agents' preferences such that they have preferences directly over the characteristics of other agents, and not the agents themselves as in the first chapter. I discuss the advantages that the alternative message space approach have in markets where there is incomplete information, such as when a student only discovers the characteristics of a subset of schools and thus can only rank those schools if asked to directly submit a ranking. I then study the effects of switching the agents' reports from a traditional matching framework where agents would submit the ranking directly over the schools they have discovered to one in which they instead submit their preferences through the alternative message space. I consider the implications of such a switch with two of the most well-known and widely used matching algorithms, deferred acceptance and the Boston mechanism. I find that any individual agent, if that agent is the only agent asked to switch from one report type to the other and if the matching algorithm is deferred acceptance, will prefer the match he receives by reporting preferences through the alternative message space. I find that if the matching algorithm is the Boston mechanism, the agent may still prefer the outcome from directly submitting his ranking over the subset. I also consider asking all agents to switch simultaneously from one method of eliciting preferences to the other, as if the market designer suddenly implemented an alternative message space in the market. I find that with either matching algorithm, there may be an agent who preferred their outcome prior to the switch, showing that such a switch does not always result in a Pareto improved outcome, even if it may in some cases. Finally, I show that under specific conditions, where each seat at each school is full and where students have preferences on characteristics such that they agree on a common ranking of schools, switching from direct reporting of rankings to the alternative message space will always result in an outcome that is not Pareto comparable to the outcome under direct reporting. I discuss the implications of these results for market designers, especially the likelihood of resistance to changing the report type. I find that while there are benefits to switching, such as reduced need for individual agents to spend resources discovering the characteristics of potential matches, market designers are likely to encounter resistance to such a change and will need to carefully consider asking agents to switch methods. Using an alternative message space where agents submit preferences over characteristics of others allows the market designer to gather information from the agents and use that information on their behalf to generate a preference ranking for them. The designer must decide how much, if any, of this information to share with the agents in the market. In Chapter 3, I collect survey data by randomly assigning respondents to a control group and two treatment groups to test if sharing all or some of the designer's information affects how agents report their preferences over characteristics. In the survey, I use characteristics of potential romantic partners, allowing the first treatment group to see all potential partners and their characteristics, the second to see only some of the potential partners and all of their characteristics and the control group to see no potential partners. The treatment groups are required to rank directly the potential partners they are shown, then asked to give their preferences over the characteristics themselves by answering binary-choice questions about each one and ranking their importance. The control group is only for their preferences over the characteristics. I find that there is some significant evidence, though somewhat weak, that exposing the agents to the information about their potential partners does change how they report their preferences over characteristics. Using an alternative message space that elicits preferences over the characteristics creates a restriction on the set of preference rankings that can be generated for the agents. With my data, I am also able to test if the rankings submitted by the treatment groups fall into the set that satisfies this restriction. I find that overwhelmingly they do not. In fact, only a very small portion of the respondents selected the same most preferred potential partner as was generated by their answers to the questions regarding their preferences over characteristics. While this result in limited in scope by the particular features of the survey, it does offer some suggestive evidence that the restriction on the set of preference rankings that can be generated may be an important one in some markets.
Issue Date:2016-07-06
Rights Information:Copyright 2016 Thomas Sahajdack
Date Available in IDEALS:2016-11-10
Date Deposited:2016-08

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