Social Welfare in One-Sided Matching Mechanisms

We study the Price of Anarchy of mechanisms for the well-known problem of one-sided matching, or house allocation, with respect to the social welfare objective. We consider both ordinal mechanisms, where agents submit preference lists over the items, and cardinal mechanisms, where agents may submit numerical values for the items being allocated. We present a general lower bound of $\Omega(\sqrt{n})$ on the Price of Anarchy, which applies to all mechanisms. We show that two well-known mechanisms, Probabilistic Serial, and Random Priority, achieve a matching upper bound. We extend our lower bound to the Price of Stability of a large class of mechanisms that satisfy a common proportionality property, and show stronger bounds on the Price of Anarchy of all deterministic mechanisms

Approximate Strategyproofness

The standard approach of mechanism design theory insists on equilibrium behavior by participants. This assumption is captured by imposing incentive constraints on the design space. But in bridging from theory to practice, it often becomes necessary to relax incentive constraints in order to allow tradeoffs with other desirable properties. This article surveys a number of different options that can be adopted in relaxing incentive constraints, providing a current view of the state-of-the-art.Engineering and Applied Science

Curing What Ails Us: How the Lessons of Behavioral Economics Can Improve Health Care Markets

The Supreme Court\u27s decision to consider the constitutionality of the Patient Protection and Affordable Care Act (Affordable Care Act or ACA) has catapulted the policy debate over health care into a new chapter fraught with profound questions about the nature of American federalism. Even as the constitutional debate takes center stage, it is worth remembering that the Obama Administration chose to frame its reform bill as a practical solution to the country\u27s mounting fiscal challenges. As policy makers begin building the administrative machinery that will give life to the Affordable Care Act, it is worth evaluating their efforts with the law\u27s fiscal goals in mind. The White House framed its arguments in favor of health care reform by insisting that effective control of the nation\u27s ballooning deficit would be impossible without reining in skyrocketing health care costs. Peter Orszag, head of the White House Office of Management and Budget from January 2009 through July 2010, spent nearly the entirety of his term as director of the Congressional Budget Office fine- tuning the health reform is deficit reform argument. As Orszag argued in testimony before the Senate Finance Committee, The rate at which health care costs grow relative to national income-rather than the aging of the population-will be the most important determinant of future federal spending. U.S. health care costs now constitute a share of our gross domestic product (GDP) that is 7.9 percentage points higher than the average for other countries in the Organization for Economic Cooperation and Development. The ability of health care reformers to effectively control costs will be one of the central public- policy challenges of the coming decade

Practical algorithms and experimentally validated incentives for equilibrium-based fair division (A-CEEI)

Approximate Competitive Equilibrium from Equal Incomes (A-CEEI) is an equilibrium-based solution concept for fair division of discrete items to agents with combinatorial demands. In theory, it is known that in asymptotically large markets: 1. For incentives, the A-CEEI mechanism is Envy-Free-but-for-Tie-Breaking (EF-TB), which implies that it is Strategyproof-in-the-Large (SP-L). 2. From a computational perspective, computing the equilibrium solution is unfortunately a computationally intractable problem (in the worst-case, assuming $\textsf{PPAD}\ne \textsf{FP}$). We develop a new heuristic algorithm that outperforms the previous state-of-the-art by multiple orders of magnitude. This new, faster algorithm lets us perform experiments on real-world inputs for the first time. We discover that with real-world preferences, even in a realistic implementation that satisfies the EF-TB and SP-L properties, agents may have surprisingly simple and plausible deviations from truthful reporting of preferences. To this end, we propose a novel strengthening of EF-TB, which dramatically reduces the potential for strategic deviations from truthful reporting in our experiments. A (variant of) our algorithm is now in production: on real course allocation problems it is much faster, has zero clearing error, and has stronger incentive properties than the prior state-of-the-art implementation.Comment: To appear in EC 202

Incentives in One-Sided Matching Problems With Ordinal Preferences

One of the core problems in multiagent systems is how to efficiently allocate a set of indivisible resources to a group of self-interested agents that compete over scarce and limited alternatives. In these settings, mechanism design approaches such as matching mechanisms and auctions are often applied to guarantee fairness and efficiency while preventing agents from manipulating the outcomes. In many multiagent resource allocation problems, the use of monetary transfers or explicit markets are forbidden because of ethical or legal issues. One-sided matching mechanisms exploit various randomization and algorithmic techniques to satisfy certain desirable properties, while incentivizing self-interested agents to report their private preferences truthfully. In the first part of this thesis, we focus on deterministic and randomized matching mechanisms in one-shot settings. We investigate the class of deterministic matching mechanisms when there is a quota to be fulfilled. Building on past results in artificial intelligence and economics, we show that when preferences are lexicographic, serial dictatorship mechanisms (and their sequential dictatorship counterparts) characterize the set of all possible matching mechanisms with desirable economic properties, enabling social planners to remedy the inherent unfairness in deterministic allocation mechanisms by assigning quotas according to some fairness criteria (such as seniority or priority). Extending the quota mechanisms to randomized settings, we show that this class of mechanisms are envyfree, strategyproof, and ex post efficient for any number of agents and objects and any quota system, proving that the well-studied Random Serial Dictatorship (RSD) is also envyfree in this domain. The next contribution of this thesis is providing a systemic empirical study of the two widely adopted randomized mechanisms, namely Random Serial Dictatorship (RSD) and the Probabilistic Serial Rule (PS). We investigate various properties of these two mechanisms such as efficiency, strategyproofness, and envyfreeness under various preference assumptions (e.g. general ordinal preferences, lexicographic preferences, and risk attitudes). The empirical findings in this thesis complement the theoretical guarantees of matching mechanisms, shedding light on practical implications of deploying each of the given mechanisms. In the second part of this thesis, we address the issues of designing truthful matching mechanisms in dynamic settings. Many multiagent domains require reasoning over time and are inherently dynamic rather than static. We initiate the study of matching problems where agents' private preferences evolve stochastically over time, and decisions have to be made in each period. To adequately evaluate the quality of outcomes in dynamic settings, we propose a generic stochastic decision process and show that, in contrast to static settings, traditional mechanisms are easily manipulable. We introduce a number of properties that we argue are important for matching mechanisms in dynamic settings and propose a new mechanism that maintains a history of pairwise interactions between agents, and adapts the priority orderings of agents in each period based on this history. We show that our mechanism is globally strategyproof in certain settings (e.g. when there are 2 agents or when the planning horizon is bounded), and even when the mechanism is manipulable, the manipulative actions taken by an agent will often result in a Pareto improvement in general. Thus, we make the argument that while manipulative behavior may still be unavoidable, it is not necessarily at the cost to other agents. To circumvent the issues of incentive design in dynamic settings, we formulate the dynamic matching problem as a Multiagent MDP where agents have particular underlying utility functions (e.g. linear positional utility functions), and show that the impossibility results still exist in this restricted setting. Nevertheless, we introduce a few classes of problems with restricted preference dynamics for which positive results exist. Finally, we propose an algorithmic solution for agents with single-minded preferences that satisfies strategyproofness, Pareto efficiency, and weak non-bossiness in one-shot settings, and show that even though this mechanism is manipulable in dynamic settings, any unilateral deviation would benefit all participating agents

Matching with Couples: Stability and Incentives in Large Markets

Accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists, because couples view pairs of jobs as complements. A stable matching may not exist when couples are present. We find conditions under which a stable matching exists with high probability in large markets. We present a mechanism that finds a stable matching with high probability, and which makes truth-telling by all participants an approximate equilibrium. We relate these theoretical results to the job market for psychologists, in which stable matchings exist for all years of the data, despite the presence of couples.