Matching with Couples Revisited

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists

The Hospitals/Residents Problem with Couples: complexity and integer programming models

The Hospitals / Residents problem with Couples (hrc) is a generalisation of the classical Hospitals / Residents problem (hr) that is important in practical applications because it models the case where couples submit joint preference lists over pairs of (typically geographically close) hospitals. In this paper we give a new NP-completeness result for the problem of deciding whether a stable matching exists, in highly restricted instances of hrc, and also an inapproximability bound for finding a matching with the minimum number of blocking pairs in equally restricted instances of hrc. Further, we present a full description of the first Integer Programming model for finding a maximum cardinality stable matching in an instance of hrc and we describe empirical results when this model applied to randomly generated instances of hrc

An Approximate "Law of One Price" in Random Assignment Games

Assignment games represent a tractable yet versatile model of two-sided markets with transfers. We study the likely properties of the core of randomly generated assignment games. If the joint productivities of every firm and worker are i.i.d bounded random variables, then with high probability all workers are paid roughly equal wages, and all firms make similar profits. This implies that core allocations vary significantly in balanced markets, but that there is core convergence in even slightly unbalanced markets. For the benchmark case of uniform distribution, we provide a tight bound for the workers' share of the surplus under the firm-optimal core allocation. We present simulation results suggesting that the phenomena analyzed appear even in medium-sized markets. Finally, we briefly discuss the effects of unbounded distributions and the ways in which they may affect wage dispersion

Essays on Matching and Market Design.

Using a combination of experimental, theoretical, computational and empirical methods, my dissertation studies matching and market design with applications to education policy including school choice and college admissions. I tackle three problems: the effect of standardized tests on matching mechanisms (Chapter 2); experimental evidence of matching in a large market (Chapter 3); and quasi-experimental evidence of the theoretical properties of matching mechanisms (Chapter 4). In Chapter 2, I investigate the matching of college admissions, where students' admission priorities and colleges' preferences over students are misaligned, due the imperfect measure of student aptitudes by standardized entrance tests. I show that in this case any matching mechanism that is stable with regard to priority is not stable with regard to preference. The resulting instability leads to market unraveling. However, a manipulable mechanism, combined with limited information about priorities, may succeed in mending this market failure. A laboratory experiment confirms this theoretical prediction. In Chapter 3, we study the role market size plays in school choice. We evaluate the performance of the Boston and the Deferred Acceptance (DA) mechanism in laboratory with different market sizes. The results show that increasing the market size from 4 to 40 students per match increases participant truth-telling under the DA but decreases it under the Boston mechanism, leading to a decrease in efficiency but no change in the large stability advantage of the DA over the Boston mechanism. Furthermore, increasing the scale to 4,000 students per match has no effect on either individual behavior or mechanism performance. Our results indicate that "large market" in practice is smaller than in theory. In Chapter 4, we evaluate the Immediate Acceptance (Boston) mechanism and the parallel mechanism in college admissions, both in the laboratory and with naturally-occurring data. Through both channels, we find that the more emphasis a mechanism put on the first choice, the more likely students rely on their rankings in the test to manipulate their reported preferences, which confirms the theoretical predictions. Although in the laboratory, the parallel mechanism proves to be more stable, we do not observe economically significant difference in stability in the field.PhDInformationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113391/1/mjng_1.pd

Approaches to mechanism design with boundedly rational agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Economics, 2012.Cataloged from PDF version of thesis.Includes bibliographical references.This dissertation ties together three papers on mechanism design with boundedly rational agents. These papers explore theoretically whether, and to what extent, limitations on agents' ability to strategically misrepresent their preferences can help a mechanism designer achieve outcomes that she could not achieve with perfectly rational agents. The first chapter investigates whether local incentive constraints are sufficient to logically imply full incentive-compatibility, in a variety of mechanism design settings. This can be motivated by a boundedly rational model in which agents cannot contemplate all possible misrepresentations, but can consider those that are close to their true preferences. This chapter offers a unified approach that covers both continuous and discrete type spaces, showing that in many commonly studied cases, local incentive-compatibility (suitably defined) implies full incentive-compatibility. The second chapter advances the methodology of looking quantitatively at incentives for strategic behavior, motivated by the premise that agents will be truthful if the incentive to be strategic is small enough. This chapter defines a mechanism's susceptibility to manipulation as the maximum amount of expected utility any agent can ever gain from strategic misrepresntation. This measure of susceptibility is then applied to anonymous voting rules. One set of results estimates the susceptibility of specific voting rules; an important finding is that several voting systems previously identified as resistant to manipulation are actually more susceptible than simple plurality rule, by the measure proposed here. A second set of results gives asymptotic lower bounds on susceptibility for any possible voting rule, under various combinations of efficiency, regularity, and informational conditions. These results illustrate how one can quantitatively explore the tradeoffs between susceptibility and other properties of the voting rule. The third chapter carries the methodology of the second chapter to a market environment: unit-demand, private-value double auction markets. This chapter quantitatively studies the tradeoff between inefficiency and susceptibility to manipulation, among all possible mechanisms for such markets. The main result approximately locates the possibility frontier, pinning it down within a factor that is logarithmic in the size of the market.by Gabriel D. Carroll.Ph.D

Characterizing and Leveraging Social Phenomena in Online Networks

Social phenomena have been studied extensively in small scales by social scientists. With the increasing popularity of Web 2.0 and online social networks/media, a large amount of data on social phenomena have become available. In this dissertation we study online social phenomena such as social influence in social networks in various contexts. This dissertation has two major components: 1. Identifying and characterizing online social phenomena 2. Leveraging online social phenomena for economic and commercial purposes. We begin the dissertation by developing multi-level revenue sharing schemes for viral marketing on social networks. Viral marketing leverages social influence among users of the social network. For our proposed models, we develop results on the computational complexity, individual rationality, and potential reach of employing the Shapley value as a revenue sharing scheme. Our results indicate that under the multi-level tree-based propagation model, the Shapley value is a promising scheme for revenue sharing, whereas under other models there are computational or incentive compatibility issues that remain open. We continue with another application of social influence: social advertising. Social advertising is a new paradigm that is utilized by online social networks. Social advertising is based in the premise that social influence can be leveraged to place ads more efficiently. The goal of our work is to understand how social ads can affect click-through rates in social networks. We propose a formal model for social ads in the context of display advertising. In our model, ads are shown to users one after the other. The probability of a user clicking an ad depends on the users who have clicked this ad so far. This information is presented to users as a social cue, thus the click probability is a function of this cue. We introduce the social display optimization problem: suppose an advertiser has a contract with a publisher for showing some number (say B) impressions of an ad. What strategy should the publisher use to show these ads so as to maximize the expected number of clicks? We show hardness results for this problem and in light of the general hardness results, we develop heuristic algorithms and compare them to natural baseline ones. We then study distributed content curation on the Web. In recent years readers have turned to the social web to consume content. In other words, they rely on their social network to curate content for them as opposed to the more traditional way of relying on news editors for this purpose -- this is an implicit consequence of social influence as well. We study how efficient this is for users with limited budgets of attention. We model distributed content curation as a reader-publisher game and show various results. Our results imply that in the complete information setting, when publishers maximize their utility selfishly, distributed content curation reaches an equilibrium which is efficient, that is, the social welfare is a constant factor of that under an optimal centralized curation. Next, we initiate the study of an exchange market problem without money that is a natural generalization of the well-studied kidney exchange problem. From the practical point of view, the problem is motivated by barter websites on the Internet, e.g., swap.com, and u-exchange.com. In this problem, the users of the social network wish to exchange items with each other. A mechanism specifies for each user a set of items that she gives away, and a set of items that she receives. Consider a set of agents where each agent has some items to offer, and wishes to receive some items from other agents. Each agent would like to receive as many items as possible from the items that she wishes, that is, her utility is equal to the number of items that she receives and wishes. However, she will have a large dis-utility if she gives away more items than what she receives, because she considers such a trade to be unfair. To ensure voluntary participation (also known as individual rationality), we require the mechanism to avoid this. We consider different variants of this problem: with and without a constraint on the length of the exchange cycles and show different results including their truthfulness and individual rationality. In the other main component of this thesis, we study and characterize two other social phenomena: 1. friends vs. the crowd and 2. altruism vs. reciprocity in social networks. More specifically, we study how a social network user's actions are influenced by her friends vs. the crowd's opinion. For example, in social rating websites where both ratings from friends and average ratings from everyone is available, we study how similar one's ratings are to each other. In the next part, we aim to analyze the motivations behind users' actions on online social media over an extended period of time. We look specifically at users' likes, comments and favorite markings on their friends' posts and photos. Most theories of why people exhibit prosocial behavior isolate two distinct motivations: Altruism and reciprocity. In our work, we focus on identifying the underlying motivations behind users' prosocial giving on social media. In particular, our goal is to identify if the motivation is altruism or reciprocity. For that purpose, we study two datasets of sequence of users' actions on social media: a dataset of wall posts by users of Facebook.com, and another dataset of favorite markings by users of Flickr.com. We study the sequence of users' actions in these datasets and provide several observations on patterns related to their prosocial giving behavior