Related papers: Opting Into Optimal Matchings
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…
We study a sequential decision-making model where a set of items is repeatedly matched to the same set of agents over multiple rounds. The objective is to determine a sequence of matchings that either maximizes the utility of the least…
Motivated by kidney exchange, we study the following mechanism-design problem: On a directed graph (of transplant compatibilities among patient-donor pairs), the mechanism must select a simple path (a chain of transplantations) starting at…
In the query-commit problem we are given a graph where edges have distinct probabilities of existing. It is possible to query the edges of the graph, and if the queried edge exists then its endpoints are irrevocably matched. The goal is to…
Matching algorithms are used routinely to match donors to recipients for solid organs transplantation, for the assignment of medical residents to hospitals, record linkage in databases, scheduling jobs on machines, network switching, online…
In preference modelling, it is essential to determine the number of questions and their arrangements to ask from the decision maker. We focus on incomplete pairwise comparison matrices, and provide the optimal filling in patterns, which…
In multi-objective optimization, a single decision vector must balance the trade-offs between many objectives. Solutions achieving an optimal trade-off are said to be Pareto optimal: these are decision vectors for which improving any one…
The problem of designing a profit-maximizing, Bayesian incentive compatible and individually rational mechanism with flexible consumers and costly heterogeneous supply is considered. In our setup, each consumer is associated with a…
We study mechanisms that select a subset of the vertex set of a directed graph in order to maximize the minimum indegree of any selected vertex, subject to an impartiality constraint that the selection of a particular vertex is independent…
We study a natural combinatorial pricing problem for sequentially arriving buyers with equal budgets. Each buyer is interested in exactly one pair of items and purchases this pair if and only if, upon arrival, both items are still available…
This paper addresses the problem of maximizing the expected size of a matching in the case of unreliable vertices and/or edges. The assumption is that upon failure, remaining vertices that have not been matched may be subject to a new…
We consider multi-item exchange markets in which agents want to receive one of their target bundles of resources. The model encompasses well-studied markets for kidney exchange, lung exchange, and multi-organ exchange. We identify a general…
Constrained maximization of submodular functions poses a central problem in combinatorial optimization. In many realistic scenarios, a number of agents need to maximize multiple submodular objectives over the same ground set. We study such…
We define and study greedy matchings in vertex-ordered bipartite graphs. It is shown that each vertex-ordered bipartite graph has a unique greedy matching. The proof uses (a weak form of) Newman's lemma. The vertex ordering is called a…
We study distributed algorithms that find a maximal matching in an anonymous, edge-coloured graph. If the edges are properly coloured with $k$ colours, there is a trivial greedy algorithm that finds a maximal matching in $k-1$ synchronous…
We explore the possibility of designing matching mechanisms that can accommodate non-standard choice behavior. We pin down the necessary and sufficient conditions on participants' choice behavior for the existence of stable and incentive…
The semi-random graph process is a single player game in which the player is initially presented an empty graph on $n$ vertices. In each round, a vertex $u$ is presented to the player independently and uniformly at random. The player then…
We consider a model for repeated stochastic matching where compatibility is probabilistic, is realized the first time agents are matched, and persists in the future. Such a model has applications in the gig economy, kidney exchange, and…
We study the problem of dynamic matching in heterogeneous networks, where agents are subject to compatibility restrictions and stochastic arrival and departure times. In particular, we consider networks with one type of easy-to-match agents…
We consider a matching problem, which is meaningful in team competitions, as well as in information theory, recommender systems, and assignment problems. In the competitions which we study, each competitor in a team order plays a match with…