Social welfare in one-sided matchings: Random priority and beyond

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-expectation) mechanisms is upper bounded by O(n^{-1/2}), indicating that random priority is asymptotically the best truthful-in-expectation mechanism and the best ordinal mechanism for the problem.Comment: 13 page

Truthful Facility Assignment with Resource Augmentation: An Exact Analysis of Serial Dictatorship

We study the truthful facility assignment problem, where a set of agents with private most-preferred points on a metric space are assigned to facilities that lie on the metric space, under capacity constraints on the facilities. The goal is to produce such an assignment that minimizes the social cost, i.e., the total distance between the most-preferred points of the agents and their corresponding facilities in the assignment, under the constraint of truthfulness, which ensures that agents do not misreport their most-preferred points. We propose a resource augmentation framework, where a truthful mechanism is evaluated by its worst-case performance on an instance with enhanced facility capacities against the optimal mechanism on the same instance with the original capacities. We study a very well-known mechanism, Serial Dictatorship, and provide an exact analysis of its performance. Although Serial Dictatorship is a purely combinatorial mechanism, our analysis uses linear programming; a linear program expresses its greedy nature as well as the structure of the input, and finds the input instance that enforces the mechanism have its worst-case performance. Bounding the objective of the linear program using duality arguments allows us to compute tight bounds on the approximation ratio. Among other results, we prove that Serial Dictatorship has approximation ratio $g/(g-2)$ when the capacities are multiplied by any integer $g \geq 3$. Our results suggest that even a limited augmentation of the resources can have wondrous effects on the performance of the mechanism and in particular, the approximation ratio goes to 1 as the augmentation factor becomes large. We complement our results with bounds on the approximation ratio of Random Serial Dictatorship, the randomized version of Serial Dictatorship, when there is no resource augmentation

Learning Riders\u27 Preferences in Ridesharing Platforms

Ridesharing platforms allow people to commute more efficiently. Ridesharing can be beneficial since it can reduce the travel expenses for individuals as well as decrease the overall traffic gridlocks. One of the key aspects of ridesharing platforms is for riders to find suitable partners to share the ride. Thus, the riders need to be matched to other riders/drivers. From the social perspective, a rider may prefer to share the ride with certain individuals as opposed to other riders. This leads to the rider having preferences over the other riders. A matching based on social welfare indicates the quality of the rides. Our goal is to maximize social welfare or the quality of rides for all riders. In order to match the riders, we need to know the preferences of the riders. However, the preferences are often unknown. To tackle these situations, we introduce a ridesharing model that implements reinforcement learning algorithms to learn the utilities of the riders based on the riders\u27 previous experiences. We investigate a variety of measures for assessing social welfare, including utilitarian, egalitarian, Nash, and leximin social welfare. Additionally, we also compute the number of strong and weak blocking pairs in each socially optimal matching to compare the stability of these matchings. We provide a comparison between two reinforcement learning algorithms: ε-greedy and UCB1, for learning utilities of the riders, maximizing social welfare, and the number of blocking pairs in the socially optimal matching. The ε-greedy algorithm with ε=0.1 provides the maximum accuracy in learning the utilities of the riders as compared to ε=0.0, ε=0.01, and UCB1 algorithm. It also provides a fewer number of blocking pairs suggesting more stability in the socially optimal matching than other reinforcement learning algorithms. However, the UCB1 algorithm outperforms all other reinforcement learning algorithms to provide maximum welfare in socially optimal matchings

Stable Fractional Matchings

We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable fractional matchings can have much higher social welfare than stable integral ones, our goal is to understand the computational complexity of finding an optimal (i.e., welfare-maximizing) or nearly-optimal stable fractional matching. We present simple approximation algorithms for this problem with weak welfare guarantees and, rather unexpectedly, we furthermore show that achieving better approximations is hard. This computational hardness persists even for approximate stability. To the best of our knowledge, these are the first computational complexity results for stable fractional matchings. En route to these results, we provide a number of structural observations

Computational Explorations of Information and Mechanism Design in Markets

Markets or platforms assemble multiple selfishly-motivated and strategic agents. The outcomes of such agent interactions depend heavily on the rules, regulations, and norms of the platform, as well as the information available to agents. This thesis investigates the design and analysis of mechanisms and information structures through the ``computational lens\u27\u27 in both static and dynamic settings. It both addresses the outcome of single platforms and fills a gap in the study of the dynamics of multiple platform interactions. In static market settings, we are particularly interested in the role of information, because mechanisms are harder to change than the information available to participants. We approach information design through specific examples, i.e., matching markets and auction markets. First, in matching markets, we study the situation where the matching is preceded by a costly interviewing stage in which firms acquire information about the qualities of candidates. We focus on the impact of the signals of quality available prior to the interviewing stage. We show that more ``commonality\u27\u27 in the quality of information can be harmful, yielding fewer matches. Second, in auction markets, we design an information environment for revenue enhancement in a sealed-bid second price auction. Much of the previous literature has focused on signal design in settings where bidders are symmetrically informed, or on the design of optimal mechanisms under fixed information structures. Here, we provide new theoretical insights for complex situations like corporate mergers, where the sender of the signal has the opportunity to communicate in different ways to different receivers. Next, in dynamic markets, we focus on two dimensions: (1) the effects of different market-clearing rules on market outcomes and (2) the dynamics of multiple platform interactions. Considering both dimensions, we investigate two important real-world dynamic markets: kidney exchange and financial markets. Specifically, in kidney exchange, we analyze the performance of different market-clearing algorithms and design a competing-market model to quantify the social welfare loss caused by market competition and exchange fragmentation. Here, we present the first analysis of equilibrium behavior in these dynamic competing matching market systems, from the viewpoints of both agents and markets. To improve the performance of kidney exchange in terms of both social welfare and individual utility, we analyze the benefit of convincing directed donation pairs to participate in paired kidney exchange, measured in terms of long-term graft survival. We provide the first empirical evidence that including compatible pairs dramatically benefits both social welfare and individual outcomes. For financial markets, in the debate over high frequency trading, the frequent call (Call) mechanism has recently received considerable attention as a proposal for replacing the continuous double auction (CDA) mechanisms that currently run most financial markets. We examine agents\u27 profit under CDA and frequent call auctions in a dynamic environment. We design an agent-based model to study the competition between these two market policies and show that CALL markets can drive trade away from CDAs. The results help to inform this very important debate