For the assignment problem where multiple indivisible items are allocated to a group of agents given their ordinal preferences, we design randomized mechanisms that satisfy first-choice maximality (FCM), i.e., maximizing the number of agents assigned their first choices, together with Pareto efficiency (PE). Our mechanisms also provide guarantees of ex-ante and ex-post fairness. The generalized eager Boston mechanism is ex-ante envy-free, and ex-post envy-free up to one item (EF1). The generalized probabilistic Boston mechanism is also ex-post EF1, and satisfies ex-ante efficiency instead of fairness. We also show that no strategyproof mechanism satisfies ex-post PE, EF1, and FCM simultaneously. In doing so, we expand the frontiers of simultaneously providing efficiency and both ex-ante and ex-post fairness guarantees for the assignment problem.

In the assignment problem, the goal is to assign indivisible items to agents who have ordinal preferences, efficiently and fairly, in a strategyproof manner. In practice, first-choice maximality, i.e., assigning a maximal number of agents their top items, is often identified as an important efficiency criterion and measure of agents' satisfaction. In this paper, we propose a natural and intuitive efficiency property, favoring-eagerness-for-remaining-items (FERI), which requires that each item is allocated to an agent who ranks it highest among remaining items, thereby implying first-choice maximality. Using FERI as a heuristic, we design mechanisms that satisfy ex-post or ex-ante variants of FERI together with combinations of other desirable properties of efficiency (Pareto-efficiency), fairness (strong equal treatment of equals and sd-weak-envy-freeness), and strategyproofness (sd-weak-strategyproofness). We also explore the limits of FERI mechanisms in providing stronger efficiency, fairness, or strategyproofness guarantees through impossibility results.

In the assignment problem, items must be assigned to agents who have unit demands, based on agents' ordinal preferences. Often the goal is to design a mechanism that is both fair and efficient. In this paper, we first prove that, unfortunately, the desirable efficiency notions rank-maximality, ex-post favoring-higher-ranks, and ex-ante favoring-higher-ranks, which aim to allocate each item to agents who rank it highest over all the items, are incompatible with the desirable fairness notions strong equal treatment of equals (SETE) and sd-weak-envy-freeness (sd-WEF) simultaneously. In light of this, we propose novel properties of efficiency based on a subtly different notion to favoring higher ranks, by favoring "eagerness" for remaining items and aiming to guarantee that each item is allocated to agents who rank it highest among remaining items. We prove that the eager Boston mechanism satisfies ep-FERI and sd-WSP, and that the uniform probabilistic respecting eagerness mechanism satisfies ea-FERI. We also prove that both mechanisms satisfy SETE and sd-WEF, and show that no mechanism can satisfy stronger versions of envyfreeness and strategyproofness while simultaneously maintaining SETE, and either ep-FERI or ea-FERI. X. Guo and Y. Cao are with Key Laboratory of High Confidence Software Technologies (MOE), Department of Computer Science and Technology, Peking University, Beijing 100871, China (e-mail: guoxiaoxi@pku.edu.cn; S. Sikdar is with Department of Computer Science, Binghamton University (email: ssikdar@binghamton.edu). H. Wang is with School of Computer Science and Cyber Engineering, Guangzhou University, China, and Key Laboratory of High Confidence Software Technologies (MOE), Department of Computer Science and Technology, Peking University, Beijing 100871, China (whpxhy@pku.edu.cn). This serves as a useful model for a variety of problems where the items may be either indivisible such as houses (Shapley and Scarf, 1974), dormitory rooms (Chen and Sönmez, 2002), and school choice without priorities (Miralles, 2009); or divisible such as natural resources like land and water (Segal-Halevi, 2016), and computational resources in cloud computing (Ghodsi et al., 2011, 2012; Grandl et al., 2014).

Several resource allocation problems involve multiple types of resources, with a different agency being responsible for "locally" allocating the resources of each type, while a central planner wishes to provide a guarantee on the properties of the final allocation given agents' preferences. We study the relationship between properties of the local mechanisms, each responsible for assigning all of the resources of a designated type, and the properties of a sequential mechanism which is composed of these local mechanisms, one for each type, applied sequentially, under lexicographic preferences, a well studied model of preferences over multiple types of resources in artificial intelligence and economics. We show that when preferences are O-legal, meaning that agents share a common importance order on the types, sequential mechanisms satisfy the desirable properties of anonymity, neutrality, non-bossiness, or Pareto-optimality if and only if every local mechanism also satisfies the same property, and they are applied sequentially according to the order O. Our main results are that under O-legal lexicographic preferences, every mechanism satisfying strategyproofness and a combination of these properties must be a sequential composition of local mechanisms that are also strategyproof, and satisfy the same combinations of properties.

A fundamental problem in multi-agent systems is resource allocation. Specifically, the problem of assigning a number of indivisible objects to agents with different preferences has been widely studied not only in multi-agent systems, but also in economics [21] and theoretical computer science [12]. The focus of our work is the special case of allocating n objects to n agents (so each agent is matched to a single object), which models many real-world applications. For example, imagine allocating office spaces to faculty members in a new building. Instead of asking each faculty member to report a full preference ranking over the available offices, the department head may ask faculty members to reveal their top choices, and then if need be, he may ask individual faculty members to reveal their next best choices, and so on. The goal of the department head is to learn a matching that satisfies some form of "economic efficiency" while asking as few queries as possible.

Partial preferences are natural in such problems since the number of bundles grows exponentially We propose multi-type probabilistic serial (MPS) with the number of types, and it is often unreasonable to expect and multi-type random priority (MRP) as extensions agents to form complete preferences over all bundles. of the well known PS and RP mechanisms Unfortunately, it is well known that no mechanism which to the multi-type resource allocation problem assigns each item fully to a single agent satisfies the basic (MTRA) with partial preferences. In our setting, fairness property of equal treatment of equals, meaning that there are multiple types of divisible items, everything else being equal, agents with the same preferences and a group of agents who have partial order should receive the same share of the resources. For example, preferences over bundles consisting of one item whenever two agents have equal and strict preferences over of each type. We show that for the unrestricted items, it is easy to see that no such mechanism satisfies equal domain of partial order preferences, no mechanism treatment of equals.

STV and ranked pairs (RP) are two well-studied voting rules for group decision-making. They proceed in multiple rounds, and are affected by how ties are broken in each round. However, the literature is surprisingly vague about how ties should be broken. We propose the first algorithms for computing the set of alternatives that are winners under some tiebreaking mechanism under STV and RP, which is also known as parallel-universes tiebreaking (PUT). Unfortunately, PUT-winners are NP-complete to compute under STV and RP, and standard search algorithms from AI do not apply. We propose multiple DFS-based algorithms along with pruning strategies, heuristics, sampling and machine learning to prioritize search direction to significantly improve the performance. We also propose novel ILP formulations for PUT-winners under STV and RP, respectively. Experiments on synthetic and real-world data show that our algorithms are overall faster than ILP.

STV and ranked pairs (RP) are two well-studied voting rules for group decision-making. They proceed in multiple rounds, and are affected by how ties are broken in each round. However, the literature is surprisingly vague about how ties should be broken. We propose the first algorithms for computing the set of alternatives that are winners under some tiebreaking mechanism under STV and RP, which is also known as parallel-universes tiebreaking (PUT). Unfortunately, PUT-winners are NP-complete to compute under STV and RP, and standard search algorithms from AI do not apply. We propose multiple DFS-based algorithms along with pruning strategies and heuristics to prioritize search direction to significantly improve the performance using machine learning. We also propose novel ILP formulations for PUT-winners under STV and RP, respectively. Experiments on synthetic and real-world data show that our algorithms are overall significantly faster than ILP, while there are a few cases where ILP is significantly faster for RP.

We study multi-type housing markets, where there are p ≥ 2 types of items, each agent is initially endowed one item of each type, and the goal is to design mechanisms without monetary transfer to (re)allocate items to the agents based on their preferences over bundles of items, such that each agent gets one item of each type. In sharp contrast to classical housing markets, previous studies in multi-type housing markets have been hindered by the lack of natural solution concepts, because the strict core might be empty. We break the barrier in the literature by leveraging AI techniques and making natural assumptions on agents’ preferences. We show that when agents’ preferences are lexicographic, even with different importance orders, the classical top-trading-cycles mechanism can be extended while preserving most of its nice properties. We also investigate computational complexity of checking whether an allocation is in the strict core and checking whether the strict core is empty. Our results convey an encouragingly positive message: it is possible to design good mechanisms for multi-type housing markets under natural assumptions on preferences.