Related papers: Algorithms for Stable Roommate with Externalities
While multi-agent trust region algorithms have achieved great success empirically in solving coordination tasks, most of them, however, suffer from a non-stationarity problem since agents update their policies simultaneously. In contrast, a…
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…
We consider the three-dimensional stable matching problem with cyclic preferences, a problem originally proposed by Knuth. Despite extensive study of the problem by experts from different areas, the question of whether every instance of…
An input to the Popular Matching problem, in the roommates setting, consists of a graph $G$ and each vertex ranks its neighbors in strict order, known as its preference. In the Popular Matching problem the objective is to test whether there…
Sequential allocation is a simple and widely studied mechanism to allocate indivisible items in turns to agents according to a pre-specified picking sequence of agents. At each turn, the current agent in the picking sequence picks its most…
House Allocations concern with matchings involving one-sided preferences, where houses serve as a proxy encoding valuable indivisible resources (e.g. organs, course seats, subsidized public housing units) to be allocated among the agents.…
This paper studies a house allocation problem in a networked housing market, where agents can invite others to join the system in order to enrich their options. Top Trading Cycle is a well-known matching mechanism that achieves a set of…
Several countries successfully use centralized matching schemes for school or higher education assignment, or for entry-level labour markets. In this paper we explore the computational aspects of a possible similar scheme for assigning…
In many applications such as rationing medical care and supplies, university admissions, and the assignment of public housing, the decision of who receives an allocation can be justified by various normative criteria. Such settings have…
The stable matching problem sets the economic foundation of several practical applications ranging from school choice and medical residency to ridesharing and refugee placement. It is concerned with finding a matching between two disjoint…
In two-sided matching markets, ensuring both stability and strategy-proofness poses a significant challenge; it is impossible when agents' preferences are unrestricted. But what if agents' preferences have specific restricted structures?…
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…
We propose an $O(n^2)$-time algorithm to determine whether a given matching is efficient in the roommates problem.
Stability is crucial in matching markets, yet in many real-world settings - from hospital residency allocations to roommate assignments - full stability is either impossible to achieve or can come at the cost of leaving many agents…
Serial dictatorship is a simple mechanism for coordinating agents in solving combinatorial optimization problems according to their preferences. The most representative such problem is one-sided matching, in which a set of n agents have…
Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently,…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
Two-sided matching markets, environments in which two disjoint groups of agents seek to partner with one another, arise in several contexts. In static, centralized markets where agents know their preferences, standard algorithms can yield a…
We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which…
It is well known that Random Serial Dictatorship is strategy-proof and leads to a Pareto-Efficient outcome. We show that this result breaks down when individuals are allowed to make transfers, and adapt Random Serial Dictatorship to…