Essays on Indices and Matching

In many decision problems, agents base their actions on a simple objective index, a single number that summarizes the available information about objects of choice independently of their particular preferences. The first chapter proposes an axiomatic approach for deriving an index which is objective and, nevertheless, can serve as a guide for decision making for decision makers with different preferences. Unique indices are derived for five decision making settings: the Aumann and Serrano (2008) index of riskiness (additive gambles), a novel generalized Sharpe ratio (for a standard portfolio allocation problem), Schreiber’s (2013) index of relative riskiness (multiplicative gambles), a novel index of delay embedded in investment cashflows (for a standard capital budgeting problem), and the index of appeal of information transactions (Cabrales et al., 2014). All indices share several attractive properties in addition to satisfying the axioms. The approach may be applicable in other settings in which indices are needed. The second chapter uses conditions from previous literature on complete orders to generate partial orders in two settings: information acquisition and segregation. In the setting of information acquisition, I show that the partialorder prior independent investment dominance (Cabrales et al., 2013) refines Blackwell’s partial order in the strict sense. In the segregation setting, I show that without the requirement of completeness, all of the axioms suggested in Frankel and Volij (2011) are satisfied simultaneously by a partial order which refines the standard partial order (Lasso de la Vega and Volij, 2014). In the third and fourth chapters, I turn to examine matching markets. Although no stable matching mechanism can induce truth-telling as a dominant strategy for all participants (Roth, 1982), recent studies have presented conditions under which truthful reporting by all agents is close to optimal (Immorlica and Mahdian, 2005; Kojima and Pathak, 2009; Lee, 2011). The third chapter demonstrates that in large, balanced, uniform markets using the Men-Proposing Deferred Acceptance Algorithm, each woman’s best response to truthful behavior by all other agents is to truncate her list substantially. In fact, the optimal degree of truncation for such a woman goes to 100% of her list as the market size grows large. Comparative statics for optimal truncation strategies in general one-to-one markets are also provide: reduction in risk aversion and reduced correlation across preferences each lead agents to truncate more. So while several recent papers focused on the limits of strategic manipulation, the results serve as a reminder that without preconditions ensuring truthful reporting, there exists a potential for significant manipulation even in settings where agents have little information. Recent findings of Ashlagi et al. (2013) demonstrate that in unbalanced random markets, the change in expected payoffs is small when one reverses which side of the market “proposes,” suggesting there is little potential gain from manipulation. Inspired by these findings, the fourth chapter studies the implications of imbalance on strategic behavior in the incomplete information setting. I show that the “long” side has significantly reduced incentives for manipulation in this setting, but that the same doesn’t always apply to the “short” side. I also show that risk aversion and correlation in preferences affect the extent of optimal manipulation as in the balanced case.Business Economic

To Infinity and Beyond: Scaling Economic Theories via Logical Compactness

Many economic-theoretic models incorporate finiteness assumptions that, while introduced for simplicity, play a real role in the analysis. Such assumptions introduce a conceptual problem, as results that rely on finiteness are often implicitly nonrobust; for example, they may depend upon edge effects or artificial boundary conditions. Here, we present a unified method that enables us to remove finiteness assumptions, such as those on market sizes, time horizons, and datasets. We then apply our approach to a variety of matching, exchange economy, and revealed preference settings. The key to our approach is Logical Compactness, a core result from Propositional Logic. Building on Logical Compactness, in a matching setting, we reprove large-market existence results implied by Fleiner's analysis, and (newly) prove both the strategy-proofness of the man-optimal stable mechanism in infinite markets and an infinite-market version of Nguyen and Vohra's existence result for near-feasible stable matchings with couples. In a trading-network setting, we prove that the Hatfield et al. result on existence of Walrasian equilibria extends to infinite markets. In a dynamic matching setting, we prove that Pereyra's existence result for dynamic two-sided matching markets extends to a doubly infinite time horizon. Finally, beyond existence and characterization of solutions, in a revealed-preference setting we reprove Reny's infinite-data version of Afriat's theorem and (newly) prove an infinite-data version of McFadden and Richter's characterization of rationalizable stochastic datasets

The redesign of the medical intern assignment mechanism in Israel

A collaboration of medical professionals with economists and computer scientists involved in “market design” had led to the redesign of the clearinghouse assigning medical students to internships in Israel. The new mechanism presents significant efficiency gains relative to the previous one, and almost all students get a better chance of getting what they want. Continued monitoring of the new mechanism is required to verify that it is not abused, and explore whether it can be improved. Other organizations in Israel may also be able to profit from the experience that accumulates from market design, both in Israel and abroad

The Large Core of College Admission Markets: Theory and Evidence

We study stable allocations in college admissions markets where students can attend the same college under different financial terms. The deferred acceptance algorithm identifies a stable allocation where funding is allocated based on merit. While merit-based stable allocations assign the same students to college, non-merit-based stable allocations may differ in the number of students assigned to college. In large markets, this possibility requires heterogeneity in applicants' sensitivity to financial terms. In Hungary, where such heterogeneity is present, a non-merit-based stable allocation would increase the number of assigned applicants by 1.9%, and affect 8.3% of the applicants relative to any merit-based stable allocation. These findings contrast sharply with findings from the matching (without contracts) literature