Nash-Bargaining-Based Models for Matching Markets: One-Sided and Two-Sided; Fisher and Arrow-Debreu

This paper addresses two deficiencies of models in the area of matching-based market design. The first arises from the recent realization that the most prominent solution that uses cardinal utilities, namely the Hylland-Zeckhauser (HZ) mechanism [Hylland and Zeckhauser, 1979], is intractable; computation of even an approximate equilibrium is PPAD-complete [Vazirani and Yannakakis, 2021; Chen et al., 2021]. The second is the extreme paucity of models that use cardinal utilities, in sharp contrast with general equilibrium theory. Our paper addresses both these issues by proposing Nash-bargaining-based matching market models. Since the Nash bargaining solution is captured by a convex program, efficiency follow; in addition, it possesses a number of desirable game-theoretic properties. Our approach yields a rich collection of models: for one-sided as well as two-sided markets, for Fisher as well as Arrow-Debreu settings, and for a wide range of utility functions, all the way from linear to Leontief. We also give very fast implementations for these models which solve large instances, with n = 2000, in one hour on a PC, even for a two-sided matching market. A number of new ideas were needed, beyond the standard methods, to obtain these implementations

Essays in Market Design

This thesis investigates the impact of incomplete information and behavioral biases in the context of market design. In chapter 2, I analyze centralized matching markets and rationalize why the arguably most heavily used mechanism in applications, the deferred acceptance mechanism, has been so successful in practice, despite the fact that it provides participants with opportunities to “game the system.” Accounting for the lack of information that participants typically have in these markets in practice, I introduce a new notion of behavior under uncertainty that captures participants’ aversion to experience regret. I show that participants optimally choose not to manipulate the deferred acceptance mechanism in order to avoid regret. Moreover, the deferred acceptance mechanism is the unique mechanism within an interesting class (quantile stable) to induce honesty from participants in this way. In chapter 3, co-authored with Leeat Yariv, we study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used deferred acceptance mechanism (Gale and Shapley, 1962). We characterize settings in which many of the results known when information is complete are overturned. In particular, small (complete-information) cores may still be associated with multiple outcomes and incentives to misreport, selection of equilibria can affect the set of individuals who are unmatched—i.e., there is no analogue for the Rural Hospital Theorem, and agents might prefer to be on the receiving side of the of the algorithm underlying the mechanism. Nonetheless, when either side of the market has assortative preferences, incomplete information does not hinder stability, and results from the complete-information setting carry through. In chapter 4, co-authored with Tatiana Mayskaya, we present a dynamic model that illustrates three forces that shape the effect of overconfidence (overprecision of consumed information) on the amount of collected information. The first force comes from overestimating the precision of the next consumed piece of information. The second force is related to overestimating the precision of already collected information. The third force reflects the discrepancy between how much information the agent expects to collect and how much information he actually collects in expectation. The first force pushes an overconfident agent to collect more information, while the second and the third forces work in the other direction. We show that under some symmetry conditions, the second and third force unequivocally dominate the first, leading to underinvestment in information.</p

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

Computing with strategic agents

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2005.Includes bibliographical references (p. 179-189).This dissertation studies mechanism design for various combinatorial problems in the presence of strategic agents. A mechanism is an algorithm for allocating a resource among a group of participants, each of which has a privately-known value for any particular allocation. A mechanism is truthful if it is in each participant's best interest to reveal his private information truthfully regardless of the strategies of the other participants. First, we explore a competitive auction framework for truthful mechanism design in the setting of multi-unit auctions, or auctions which sell multiple identical copies of a good. In this framework, the goal is to design a truthful auction whose revenue approximates that of an omniscient auction for any set of bids. We focus on two natural settings - the limited demand setting where bidders desire at most a fixed number of copies and the limited budget setting where bidders can spend at most a fixed amount of money. In the limit demand setting, all prior auctions employed the use of randomization in the computation of the allocation and prices.(cont.) Randomization in truthful mechanism design is undesirable because, in arguing the truthfulness of the mechanism, we employ an underlying assumption that the bidders trust the random coin flips of the auctioneer. Despite conjectures to the contrary, we are able to design a technique to derandomize any multi-unit auction in the limited demand case without losing much of the revenue guarantees. We then consider the limited budget case and provide the first competitive auction for this setting, although our auction is randomized. Next, we consider abandoning truthfulness in order to improve the revenue properties of procurement auctions, or auctions that are used to hire a team of agents to complete a task. We study first-price procurement auctions and their variants and argue that in certain settings the payment is never significantly more than, and sometimes much less than, truthful mechanisms. Then we consider the setting of cost-sharing auctions. In a cost-sharing auction, agents bid to receive some service, such as connectivity to the Internet. A subset of agents is then selected for service and charged prices to approximately recover the cost of servicing them.(cont.) We ask what can be achieved by cost -sharing auctions satisfying a strengthening of truthfulness called group-strategyproofness. Group-strategyproofness requires that even coalitions of agents do not have an incentive to report bids other than their true values in the absence of side-payments. For a particular class of such mechanisms, we develop a novel technique based on the probabilistic method for proving bounds on their revenue and use this technique to derive tight or nearly-tight bounds for several combinatorial optimization games. Our results are quite pessimistic, suggesting that for many problems group-strategyproofness is incompatible with revenue goals. Finally, we study centralized two-sided markets, or markets that form a matching between participants based on preference lists. We consider mechanisms that output matching which are stable with respect to the submitted preferences. A matching is stable if no two participants can jointly benefit by breaking away from the assigned matching to form a pair.(cont.) For such mechanisms, we are able to prove that in a certain probabilistic setting each participant's best strategy is truthfulness with high probability (assuming other participants are truthful as well) even though in such markets in general there are provably no truthful mechanisms.by Nicole Immorlica.Ph.D

Computing With Distributed Information

The age of computing with massive data sets is highlighting new computational challenges. Nowadays, a typical server may not be able to store an entire data set, and thus data is often partitioned and stored on multiple servers in a distributed manner. A natural way of computing with such distributed data is to use distributed algorithms: these are algorithms where the participating parties (i.e., the servers holding portions of the data) collaboratively compute a function over the entire data set by sending (preferably small-size) messages to each other, where the computation performed at each participating party only relies on the data possessed by it and the messages received by it. We study distributed algorithms focused on two key themes: convergence time and data summarization. Convergence time measures how quickly a distributed algorithm settles on a globally stable solution, and data summarization is the approach of creating a compact summary of the input data while retaining key information. The latter often leads to more efficient computation and communication. The main focus of this dissertation is on design and analysis of distributed algorithms for important problems in diverse application domains centering on the themes of convergence time and data summarization. Some of the problems we study include convergence time of double oral auction and interdomain routing, summarizing graphs for large-scale matching problems, and summarizing data for query processing

Learning and Robustness With Applications To Mechanism Design

The design of economic mechanisms, especially auctions, is an increasingly important part of the modern economy. A particularly important property for a mechanism is strategyproofness -- the mechanism must be robust to strategic manipulations so that the participants in the mechanism have no incentive to lie. Yet in the important case when the mechanism designer's goal is to maximize their own revenue, the design of optimal strategyproof mechanisms has proved immensely difficult, with very little progress after decades of research. Recently, to escape this impasse, a number of works have parameterized auction mechanisms as deep neural networks, and used gradient descent to successfully learn approximately optimal and approximately strategyproof mechanisms. We present several improvements on these techniques. When an auction mechanism is represented as a neural network mapping bids from outcomes, strategyproofness can be thought of as a type of adversarial robustness. Making this connection explicit, we design a modified architecture for learning auctions which is amenable to integer-programming-based certification techniques from the adversarial robustness literature. Existing baselines are empirically strategyproof, but with no way to be certain how strong that guarantee really is. By contrast, we are able to provide perfectly tight bounds on the degree to which strategyproofness is violated at any given point. Existing neural networks for auctions learn to maximize revenue subject to strategyproofness. Yet in many auctions, fairness is also an important concern -- in particular, fairness with respect to the items in the auction, which may represent, for instance, ad impressions for different protected demographic groups. With our new architecture, ProportionNet, we impose fairness constraints in addition to the strategyproofness constraints, and find approximately fair, approximately optimal mechanisms which outperform baselines. With PreferenceNet, we extend this approach to notions of fairness that are learned from possibly vague human preferences. Existing network architectures can represent additive and unit-demand auctions, but are unable to imposing more complex exactly-k constraints on the allocations made to the bidders. By using the Sinkhorn algorithm to add differentiable matching constraints, we produce a network which can represent valid allocations in such settings. Finally, we present a new auction architecture which is a differentiable version of affine maximizer auctions, modified to offer lotteries in order to potentially increase revenue. This architecture is always perfectly strategyproof (avoiding the Lagrangian-based constrained optimization of RegretNet) -- to achieve this goal, however, we need to accept that we cannot in general represent the optimal auction