Related papers: Popular b-matchings
We study stable matching problems where agents have multilayer preferences: There are $\ell$ layers each consisting of one preference relation for each agent. Recently, Chen et al. [EC '18] studied such problems with strict preferences,…
We consider stable and popular matching problems in arbitrary graphs, which are referred to as stable roommates instances. We extend the 3/2-approximation algorithm for the maximum size weakly stable matching problem to the roommates case,…
The stable marriage problem has a wide variety of practical applications, ranging from matching resident doctors to hospitals, to matching students to schools, or more generally to any two-sided market. We consider a useful variation of the…
Many-to-many matching with contracts is studied in the framework of revealed preferences. All preferences are described by choice functions that satisfy natural conditions. Under a no-externality assumption individual preferences can be…
In bipartite matching problems, agents on two sides of a graph want to be paired according to their preferences. The stability of a matching depends on these preferences, which in uncertain environments also reflect agents' beliefs about…
An approximation of strategyproofness in large, two-sided matching markets is highly evident. Through simulations, one can observe that the percentage of agents with useful deviations decreases as the market size grows. Furthermore, there…
We study the two-sided stable matching problem with one-sided uncertainty for two sets of agents A and B, with equal cardinality. Initially, the preference lists of the agents in A are given but the preferences of the agents in B are…
Two-sided matchings are an important theoretical tool used to model markets and social interactions. In many real life problems the utility of an agent is influenced not only by their own choices, but also by the choices that other agents…
A planner wants to select one agent out of n agents on the basis of a binary characteristic that is commonly known to all agents but is not observed by the planner. Any pair of agents can either be friends or enemies or impartials of each…
Given a set $A$ of $n$ people and a set $B$ of $m \geq n$ items, with each person having a list that ranks his/her preferred items in order of preference, we want to match every person with a unique item. A matching $M$ is called popular if…
Reallocating resources to get mutually beneficial outcomes is a fundamental problem in various multi-agent settings. While finding an arbitrary Pareto optimal allocation is generally easy, checking whether a particular allocation is Pareto…
In two-sided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking…
We consider the problem of stable matching with dynamic preference lists. At each time step, the preference list of some player may change by swapping random adjacent members. The goal of a central agency (algorithm) is to maintain an…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
The classical Stable Roommates problem is to decide whether there exists a matching of an even number of agents such that no two agents which are not matched to each other would prefer to be with each other rather than with their…
Consider a matching problem on a graph where disjoint sets of vertices are privately owned by self-interested agents. An edge between a pair of vertices indicates compatibility and allows the vertices to match. We seek a mechanism to…
Let $G$ be a digraph where every node has preferences over its incoming edges. The preferences of a node extend naturally to preferences over branchings, i.e., directed forests; a branching $B$ is popular if $B$ does not lose a head-to-head…
In many economic contexts, agents from a same population team up to better exploit their human capital. In such contexts (often called "roommate matching problems"), stable matchings may fail to exist even when utility is transferable. We…
Recommender systems play an increasingly crucial role in shaping people's opportunities, particularly in online dating platforms. It is essential from the user's perspective to increase the probability of matching with a suitable partner…
We consider a two-sided matching problem in which the agents on one side have dichotomous preferences and the other side representing institutions has strict preferences (priorities). It captures several important applications in matching…