We study one-sided matching problems where $n$ agents have preferences over $m$ objects and each of them need to be assigned to at most one object. Most work on such problems assume that the agents only have ordinal preferences and usually the goal in them is to compute a matching that satisfies some notion of economic efficiency. However, in reality, agents may have some preference intensities or cardinal utilities that, e.g., indicate that they like an object much more than another object, and not taking these into account can result in a loss in welfare. While one way to potentially account for these is to directly ask the agents for this information, such an elicitation process is cognitively demanding. Therefore, we focus on learning more about their cardinal preferences using simple threshold queries which ask an agent if they value an object greater than a certain value, and use this in turn to come up with algorithms that produce a matching that, for a particular economic notion $X$, satisfies $X$ and also achieves a good approximation to the optimal welfare among all matchings that satisfy $X$. We focus on several notions of economic efficiency, and look at both adaptive and non-adaptive algorithms. Overall, our results show how one can improve welfare by even non-adaptively asking the agents for just one bit of extra information per object.
We study the problem of approximate social welfare maximization (without money) in one-sided matching problems when agents have unrestricted cardinal preferences over a finite set of items. Random priority is a very well-known truthful-in-expectation mechanism for the problem. We prove that the approximation ratio of random priority is Theta(n^{-1/2}) while no truthful-in-expectation mechanism can achieve an approximation ratio better than O(n^{-1/2}), where n is the number of agents and items. Furthermore, we prove that the approximation ratio of all ordinal (not necessarily truthful-in-expec…
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 $Ω(\sqrt{n})$ 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 …
We study social welfare in one-sided matching markets where the goal is to efficiently allocate n items to n agents that each have a complete, private preference list and a unit demand over the items. Our focus is on allocation mechanisms that do not involve any monetary payments. We consider two natural measures of social welfare: the ordinal welfare factor which measures the number of agents that are at least as happy as in some unknown, arbitrary benchmark allocation, and the linear welfare factor which assumes an agent's utility linearly decreases down his preference lists, and measures th…
We study the efficiency (in terms of social welfare) of truthful and symmetric mechanisms in one-sided matching problems with {\em dichotomous preferences} and {\em normalized von Neumann-Morgenstern preferences}. We are particularly interested in the well-known {\em Random Serial Dictatorship} mechanism. For dichotomous preferences, we first show that truthful, symmetric and optimal mechanisms exist if intractable mechanisms are allowed. We then provide a connection to online bipartite matching. Using this connection, it is possible to design truthful, symmetric and tractable mechanisms that …
We study the welfare structure in two-sided large random matching markets. In the model, each agent has a latent personal score for every agent on the other side of the market and her preferences follow a logit model based on these scores. Under a contiguity condition, we provide a tight description of stable outcomes. First, we identify an intrinsic fitness for each agent that represents her relative competitiveness in the market, independent of the realized stable outcome. The intrinsic fitness values correspond to scaling coefficients needed to make a latent mutual matrix bi-stochastic, whe…
We consider the problem of welfare maximization in two-sided markets using simple mechanisms that are prior-independent. The Myerson-Satterthwaite impossibility theorem shows that even for bilateral trade, there is no feasible (IR, truthful, budget balanced) mechanism that has welfare as high as the optimal-yet-infeasible VCG mechanism, which attains maximal welfare but runs a deficit. On the other hand, the optimal feasible mechanism needs to be carefully tailored to the Bayesian prior, and is extremely complex, eluding a precise description. We present Bulow-Klemperer-style results to circum…
We design novel mechanisms for welfare-maximization in two-sided markets. That is, there are buyers willing to purchase items and sellers holding items initially, both acting rationally and strategically in order to maximize utility. Our mechanisms are designed based on a powerful correspondence between two-sided markets and prophet inequalities. They satisfy individual rationality, dominant-strategy incentive compatibility, budget-balance constraints and give constant-factor approximations to the optimal social welfare. We improve previous results in several settings: Our main focus is on mat…
The standard two-sided and one-sided matching problems, and the closely related school choice problem, have been widely studied from an axiomatic viewpoint. A small number of algorithms dominate the literature. For two-sided matching, the Gale-Shapley algorithm; for one-sided matching, (random) Serial Dictatorship and Probabilistic Serial rule; for school choice, Gale-Shapley and the Boston mechanisms. The main reason for the dominance of these algorithms is their good (worst-case) axiomatic behaviour with respect to notions of efficiency and strategyproofness. However if we shift the focus to…
This paper investigates the problem of proportionally fair double sided energy auction involving buying and selling agents. The grid is assumed to be operating under islanded mode. A distributed auction algorithm that can be implemented by an aggregator, as well as a possible approach by which the agents may approximate price anticipation is considered. Equilibrium conditions arising due to price anticipation is analyzed. A modified auction to mitigate the resulting loss in efficiency due to such behavior is suggested. This modified auction allows the aggregate social welfare of the agents to …
We study the problem of allocating indivisible goods among $n$ agents with the objective of maximizing Nash social welfare (NSW). This welfare function is defined as the geometric mean of the agents' valuations and, hence, it strikes a balance between the extremes of social welfare (arithmetic mean) and egalitarian welfare (max-min value). Nash social welfare has been extensively studied in recent years for various valuation classes. In particular, a notable negative result is known when the agents' valuations are complement-free and are specified via value queries: for XOS valuations, one nec…
State-of-the-art posted-price mechanisms for submodular bidders with $m$ items achieve approximation guarantees of $O((\log \log m)^3)$ [Assadi and Singla, 2019]. Their truthfulness, however, requires bidders to compute an NP-hard demand-query. Some computational complexity of this form is unavoidable, as it is NP-hard for truthful mechanisms to guarantee even an $m^{1/2-\varepsilon}$-approximation for any $\varepsilon > 0$ [Dobzinski and Vondrák, 2016]. Together, these establish a stark distinction between computationally-efficient and communication-efficient truthful mechanisms. We show that…
Learn to Match: Two-Sided Matching with Temporally Extended Feedback
Department of Economics, University of Washington（华盛顿大学经济系）；Paul G. Allen School of Computer Science & Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
We consider two sided matching markets consisting of agents with non-transferable utilities; agents from the opposite sides form matching pairs (e.g., buyers-sellers) and negotiate the terms of their math which may include a monetary transfer. Competitive equilibria are the elements of the core of this game. We present the first combinatorial characterization of competitive equilibria that relates the utility of each agent at equilibrium to the equilibrium utilities of other agents in a strictly smaller market excluding that agent; thus automatically providing a constructive proof of existence…
We study the problem of allocating indivisible goods among agents in a fair and economically efficient manner. In this context, the Nash social welfare-defined as the geometric mean of agents' valuations for their assigned bundles-stands as a fundamental measure that quantifies the extent of fairness of an allocation. Focusing on instances in which the agents' valuations have binary marginals, we develop essentially tight results for (approximately) maximizing Nash social welfare under two of the most general classes of complement-free valuations, i.e., under binary XOS and binary subadditive …
We consider the one-sided matching problem, where n agents have preferences over n items, and these preferences are induced by underlying cardinal valuation functions. The goal is to match every agent to a single item so as to maximize the social welfare. Most of the related literature, however, assumes that the values of the agents are not a priori known, and only access to the ordinal preferences of the agents over the items is provided. Consequently, this incomplete information leads to loss of efficiency, which is measured by the notion of distortion. In this paper, we further assume that …
Wuhan University（武汉大学）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Rotman School of Management, University of Toronto（多伦多大学罗特曼管理学院）；DeGroote School of Business, McMaster University（麦克马斯特大学德格罗斯特商学院）
In most social choice settings, the participating agents express their preferences over the different alternatives in the form of linear orderings. While this clearly simplifies preference elicitation, it inevitably leads to poor performance with respect to optimizing a cardinal objective, such as the social welfare, since the values of the agents remain virtually unknown. This loss in performance because of lack of information is measured by the notion of distortion. A recent array of works put forward the agenda of designing mechanisms that learn the values of the agents for a small number o…
We study mechanism design problems in the {\em ordinal setting} wherein the preferences of agents are described by orderings over outcomes, as opposed to specific numerical values associated with them. This setting is relevant when agents can compare outcomes, but aren't able to evaluate precise utilities for them. Such a situation arises in diverse contexts including voting and matching markets. Our paper addresses two issues that arise in ordinal mechanism design. To design social welfare maximizing mechanisms, one needs to be able to quantitatively measure the welfare of an outcome which is…
In this paper, we consider a mobility system of travelers and providers, and propose a "mobility game" to study when a traveler is matched to a provider. Each traveler seeks to travel using the services of only one provider, who manages one specific mode of transportation (e.g., car, bus, train, bike). The services of each provider are capacitated and can serve up to a fixed number of travelers at any instant of time. Thus, our problem falls under the category of many-to-one assignment problems, where the goal is to find the conditions that guarantee the stability of assignments. We formulate …
We study the design of a decentralized two-sided matching market in which agents' search is guided by the platform. There are finitely many agent types, each with (potentially random) preferences drawn from known type-specific distributions. Equipped with knowledge of these distributions, the platform guides the search process by determining the meeting rate between each pair of types from the two sides. Focusing on symmetric pairwise preferences in a continuum model, we first characterize the unique stationary equilibrium that arises given a feasible set of meeting rates. We then introduce th…
This paper studies the effects of altruism and spitefulness in a two-sided market in which agents behave strategically and trade according to the Shapley-Shubik mechanism. By assuming that altruistic agents have concerns for others on the opposite side of the market, it shows that agents always find advantageous to trade. However, they prefer to stay out of the market and consume their endowments when there are altruistic agents who have concerns for the welfare of those on the same side of the market, or when there are spiteful agents. These non-trade situations occur either because the neces…
Motivated by the success of the serial dictatorship mechanism in social choice settings, we explore its usefulness in tackling various combinatorial optimization problems. We do so by considering an abstract model, in which a set of agents are asked to act in a particular ordering, called the action sequence. Each agent acts in a way that gives her the maximum possible value, given the actions of the agents who preceded her in the action sequence. Our goal is to compute action sequences that yield approximately optimal total value to the agents (a.k.a., social welfare). We assume query access …
Aggregating the preferences of individuals into a collective decision is the core subject of study of social choice theory. In 2006, Procaccia and Rosenschein considered a utilitarian social choice setting, where the agents have explicit numerical values for the alternatives, yet they only report their linear orderings over them. To compare different aggregation mechanisms, Procaccia and Rosenschein introduced the notion of distortion, which quantifies the inefficiency of using only ordinal information when trying to maximize the social welfare, i.e., the sum of the underlying values of the ag…
