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A fundamental resource allocation setting is the random assignment problem in which agents express preferences over objects that are then randomly allocated to the agents. In 2001, Bogomolnaia and Moulin presented the probabilistic serial…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem, edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case…
The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) involves assigning students to projects based on student preferences over projects, lecturer preferences over students, and the maximum number of…
The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a…
We consider a problem of placing generators of rewards to be collected by randomly moving agents in a network. In many settings, the precise mobility pattern may be one of several possible, based on parameters outside our control, such as…
The \textsc{Housing Market} problem is a widely studied resource allocation problem. In this problem, each agent can only receive a single object and has preferences over all objects. Starting from an initial endowment, we want to reach a…
Efficient computability is an important property of solution concepts in matching markets. We consider the computational complexity of finding and verifying various solution concepts in trading networks-multi-sided matching markets with…
Consider the standard hospitals/residents problem, or the two-sided many-to-one stable matching problem, and assume that the true preference lists of both sides are complete and strict. The lists actually submitted, however, are truncated.…
The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) comprises three sets of agents, namely students, projects and lecturers, where students have preferences over projects and lecturers have preferences…
This paper considers a network of agents, where each agent is assumed to take actions optimally with respect to a predefined payoff function involving the latest actions of the agent's neighbors. Neighborhood relationships stem from payoff…
Allocating indivisible items among a set of agents is a frequently studied discrete optimization problem. In the setting considered in this work, the agents' preferences over the items are assumed to be identical. We consider a very recent…
We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…
We study the Student Project Allocation problem with lecturer preferences over Students (SPA-S), which involves the assignment of students to projects based on student preferences over projects, lecturer preferences over students, and…
The Hospitals/Residents problem (HR) is a many-to-one matching problem whose solution concept is stability. It is widely used in assignment systems such as assigning medical students (residents) to hospitals. To resolve imbalance in the…
The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical…
This paper investigates the stability of the least squares approximation $P_m^n$ within the univariate polynomial space of degree $m$, denoted by ${\mathbb P}_m$. The approximation $P_m^n$ entails identifying a polynomial in ${\mathbb P}_m$…
An instance of a strongly stable matching problem (SSMP) is an undirected bipartite graph $G=(A \cup B, E)$, with an adjacency list of each vertex being a linearly ordered list of ties, which are subsets of vertices equally good for a given…
The Hospital Residents setting models important problems like school choice, assignment of undergraduate students to degree programs, among many others. In this setting, fixed quotas are associated with the programs that limit the number of…
The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…