Abstract

This thesis consists of three studies on mechanism design with and without monetary transfers. Following a brief introductory chapter, the second chapter contributes to the auction design literature and studies bidders with heterogeneous risk attitudes. The third and fourth chapters focus on matching couples to jobs without monetary transfers. The third chapter proposes a new method of preference aggregation for couples that enter the labour market together, and the fourth chapter proposes a new mechanism that accommodates couples in entry-level labour markets which relies on the preference aggregation studied in the third chapter.

In the second chapter I study the sale of a single indivisible good to two bidders with heterogeneous attitudes towards risk. Optimal auctions for risk neutral or risk averse bidders have been studied in the literature, but bidders are assumed to be either risk neutral or risk averse. My objective is to study the heterogeneity of bidders in terms of their risk attitude. In my model the valuations of the bidders are private information, however, one bidder is risk averse with a
publicly known degree of risk aversion, while the other bidder is risk neutral. I derive the revenue maximizing Bayesian incentive compatible auction in this environment.

The third chapter focuses on the aggregation of a couple’s preferences over their respective jobs when they enter a centralized labor market jointly, such as the market for assigning hospital residencies to medical students. Usually in such markets couples need to submit joint preferences over pairs of residency positions. Starting from two individual preference orderings over positions, we first study the Lexicographic and the Rank-Based Leximin rules, and then propose a family of aggregation rules, the k-Lexi-Pairing rules, and provide an axiomatic characterization of these rules. The parameter k indicates the degree of selfishness for one partner (and altruism for the other partner), with the least selfish Rank Based Leximin rule at one extreme and the most selfish Lexicographic rule at the other extreme. Since couples care about geographic proximity, we also identify a simple parametric family of preference aggregation rules, (k, t)-Lexi-Pairing rules, which also reflect the couple’s preference for togetherness.

In the fourth chapter we study centralized entry-level labour markets with couples and require couples to submit only (k, t)-Lexi-Pairing joint preferences as their input to the matching procedure. We introduce a new matching mechanism which takes advantage of the known preference structure of the joint preferences submitted by couples. This mechanisms resolves the cycles that typically arise in matching procedures with couples by working with the parameter t which indicates the degree of preference to be employed in the same geographic area for a couple. We also analyze the stability and efficiency properties of this new mechanism for couples’ markets. This is the first study that takes into account how couples form their paired preference orderings when participating in a centralized matching procedure, and the first mechanism which makes explicit use of the preference aggregation parameters that indicate the preferences of couples for togetherness.