Nick Arnosti

Centralized Clearinghouse Design: A Quantity-Quality Tradeoff

Stable matching mechanisms are used to clear many two-sided markets. In practice, these mechanisms leave many agents on both sides unmatched. What factors determine the number of unmatched agents, and the quality of matches that do form? This paper answers this question, with a particular focus on how match outcomes depend on correlations in agent preferences. I consider three canonical preference structures: fully idiosyncratic preferences, common preferences (agents agree on the attractiveness of those on the opposite side), and aligned preferences (potential partners agree on the attractiveness of their match).I find that idiosyncratic preferences result in more matches than common preferences do. Perhaps more surprisingly, the case of aligned preferences results in the fewest matches. Regarding match quality, the story reverses itself: aligned preferences produce the most high quality matches, followed by common preferences. These facts have implications for the design of priority rules and tie- breaking procedures in school choice settings, as they point to a fundamental tradeoff between matching many students, and maximizing the number of students who get one of their top choices.

Cutting Plane Training for Linear Support Vector Machines

Support Vector Machines (SVMs) have been shown to achieve high performance on classification tasks across many domains, and a great deal of work has been dedicated to developing computationally efficient training algorithms for linear SVMs. One approach [1] approximately minimizes risk through use of cutting planes, and is improved by [2], [3]. We build upon this work, presenting a modification to the algorithm developed by Franc and Sonnenburg [2]. We demonstrate empirically that our changes can reduce cutting plane training time by up to 40 percent, and discuss how changes in data sets and parameter settings affect the effectiveness of our method.

Short Lists in Centralized Clearinghouses

Stable matching mechanisms are used to clear many two-sided markets. In most settings, frictions cause participants to submit short preference lists (even if there are many potentially acceptable matches). This paper studies the consequences of this fact, and focuses on two broad questions. First, when lists are short, what is the quantity and quality of matches formed through the clearinghouse? Second, what are the effects of introducing an aftermarket which allows agents left unmatched by the clearinghouse to find one another? The answers to these questions depend crucially on the extent and form of correlations in agent preferences. I consider three canonical preference structures: fully independent (or idiosyncratic) preferences, vertical preferences (agents agree on the attractiveness of those on the opposite side), and aligned preferences (potential partners agree on the attractiveness of their match). I find that when agent preferences are idiosyncratic, more matches form than when agents are vertically differentiated. Perhaps more surprisingly, I show that the case of aligned preferences causes the fewest matches to form. When considering quality of matches, the story reverses itself: aligned preferences produce the most high quality matches, followed by correlated preferences, with independent preferences producing the fewest. These facts have implications for the design of priority structures and tie-breaking procedures in school choice settings, as they point to a fundamental tradeoff between matching many students, and maximizing the number of students who get one of their top choices. Regarding the role of the aftermarket, I find that when preferences are aligned, the aftermarket unambiguously improves the welfare of both sides. In other cases, however, the introduction of an aftermarket has multiple competing effects, and may either raise or lower aggregate welfare. This suggests that when designing an aftermarket, the extent and form of correlations in agent preferences are an important factor to consider.

How (Not) to Allocate Affordable Housing

We consider a setting in which agents and items match dynamically over time. We show that repeated independent lotteries with unlimited entry (which are commonly used in practice) encourage agents to enter many lotteries, and may result in low match value. We consider three alternate mechanisms: allowing agents to save unused tickets, limiting agents to entering at most one lottery, and allocating developments using a waiting list. We show that these three mechanisms are equivalent: for each agent, the probability of matching and expected value conditioned on matching are identical. Compared to a repeated lottery, these mechanisms result in higher-quality matches for matched agents. However, in some cases, a repeated lottery is more likely to match agents with the worst outside options, and thus may outperform the other mechanisms in terms of utilitarian welfare. We discuss the implications of these findings for two systems in New York City that currently use a repeated lottery: the allocation of affordable housing and of discounted tickets to broadway shows.

The Non-Existence of Stable Mechanisms in Incomplete Information Environments

We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and preferences are known, then no group of agents can profitably deviate in this manner. We ask whether this property holds even when agents have incomplete information about their own preferences or the preferences of others. We find that it does not. In particular, when agents are uncertain about the preferences of others, every mechanism is susceptible to deviations by groups of agents. When, in addition, agents are uncertain about their own preferences, every mechanism is susceptible to deviations in which a single pair of agents agrees in advance to match to each other.

Adverse Selection and Auction Design for Internet Display Advertising

We model an online display advertising environment with brand advertisers and better-informed performance advertisers, and seek an auction mechanism that is strategy-proof, anonymous and insulates brand advertisers from adverse selection. We find that the only such mechanism that is also false-name proof assigns the item to the highest bidding performance advertiser only when the ratio of the highest bid to the second highest bid is sufficiently large. For fat-tailed match-value distributions, this new mechanism captures most of the gains from good matching and improves match values substantially compared to the common practice of setting aside impressions in advance.

Welfare-Improving Cascades and the Effect of Noisy Reviews

We study a setting in which firms produce items whose quality is ex-ante unobservable, but learned by customers over time. Firms take customer learning into account when making production decisions. We focus on the effect that the review process has on product quality. Specifically, we compare equilibrium quality levels in the setting described above to the quality that would be produced if customers could observe item quality directly. We find that in many cases, customers are better off when relying on reviews, i.e. better off in the world where they have less information. The idea behind our result is that the risk of losing future profits due to bad initial reviews may drive firms to produce an exceptional product. This intuitive insight contrasts sharply with much of the previous academic literature on the subject.