Related papers: Stable Dinner Party Seating Arrangements
We consider a coalition formation setting where each agent belongs to one of the two types, and agents' preferences over coalitions are determined by the fraction of the agents of their own type in each coalition. This setting differs from…
We introduce the problem of adapting a stable matching to forced and forbidden pairs. Specifically, given a stable matching $M_1$, a set $Q$ of forced pairs, and a set $P$ of forbidden pairs, we want to find a stable matching that includes…
We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions.…
We introduce the {\sc classified stable matching} problem, a problem motivated by academic hiring. Suppose that a number of institutes are hiring faculty members from a pool of applicants. Both institutes and applicants have preferences…
We study the fair allocation of indivisible items subject to conflict constraints. In this framework, the items are represented as the vertices of a graph, with edges corresponding to conflicts between pairs of items. Each agent is assigned…
Many countries around the world, including Korea, use the school choice lottery system. However, this method has a problem in that many students are assigned to less-preferred schools based on the lottery results. In addition, the task of…
We consider the problem of allocating indivisible objects to agents when agents have strict preferences over objects. There are inherent trade-offs between competing notions of efficiency, fairness and incentives in assignment mechanisms.…
Stable matching is a fundamental area with many practical applications, such as centralised clearinghouses for school choice or job markets. Recent work has introduced the paradigm of near-feasibility in capacitated matching settings, where…
Relying on configuration spaces and equivariant topology, we study a general "cooperative envy-free division problem". A group of players want to cut a "cake" $I=[0,1]$ and divide among themselves the pieces in an envy-free manner. Once the…
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…
We consider popular matching problems in both bipartite and non-bipartite graphs with strict preference lists. It is known that every stable matching is a min-size popular matching. A subclass of max-size popular matchings called dominant…
This paper studies the allocation of indivisible items to agents, when each agent's preferences are expressed by means of a directed acyclic graph. The vertices of each preference graph represent the subset of items approved of by the…
I provide a unified framework to establish the existence of a weak Pareto efficient, envy-free allocation in general settings: random allocations are probability measures on a compact metric space, and preferences of agents are represented…
This paper links matching markets with aligned preferences to optimal transport theory. We show that stability, efficiency, and fairness emerge as solutions to a parametric family of optimal transport problems. The parameter reflects…
Gale and Shapley introduced a matching problem between two sets of agents where each agent on one side has an exogenous preference ordering over the agents on the other side. They defined a matching as stable if no unmatched pair can both…
We study the computational complexity of finding stable outcomes in hedonic games, which are a class of coalition formation games. We restrict our attention to symmetric additively-separable hedonic games, which are a nontrivial subclass of…
Approval-based committee selection is a model of significant interest in social choice theory. In this model, we have a set of voters $\mathcal{V}$, a set of candidates $\mathcal{C}$, and each voter has a set $A_v \subset \mathcal{C}$ of…
Suppose each of $n$ men and $n$ women is located at a point in a metric space. A woman ranks the men in order of their distance to her from closest to farthest, breaking ties at random. The men rank the women similarly. An interesting…
One of the basic properties of a queueing network is stability. Roughly speaking, it is the property that the total number of jobs in the network remains bounded as a function of time. One of the key questions related to the stability issue…
The problem of dividing resources fairly occurs in many practical situations and is therefore an important topic of study in economics. In this paper, we investigate envy-free divisions in the setting where there are multiple players in…