Related papers: Stable Tables
The Stable Marriage Problem, as proposed by Gale and Shapley, considers producing a bipartite matching between two equally sized sets of boys (proposers) and respectively girls (acceptors), each member having a total preference order over…
The stable roommates problem does not necessarily have a solution, i.e. a stable matching. We had found that, for the uniformly random instance, the expected number of solutions converges to $e^{1/2}$ as $n$, the number of members, grows,…
In this paper, we study fairness in committee selection problems. We consider a general notion of fairness via stability: A committee is stable if no coalition of voters can deviate and choose a committee of proportional size, so that all…
The stable marriage problem, as addressed by Gale and Shapely [1] consists of providing a bipartite matching between n " boys " and n " girls "-each of whom have a totally ordered preference list over the other set-such that there exists no…
Consider a cyclically ordered collection of $r$ equinumerous agent sets with strict preferences of every agent over the agents from the next agent set. A weakly stable cyclic matching is a partition of the set of agents into disjoint union…
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…
Coalition formation over graphs is a well studied class of games whose players are vertices and feasible coalitions must be connected subgraphs. In this setting, the existence and computation of equilibria, under various notions of…
We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more…
The stable marriage problem has been introduced in order to describe a complex system where individuals attempt to optimise their own satisfaction, subject to mutually conflicting constraints. Due to the potential large applicability of…
We study a generalization of the classical stable matching problem that allows for cardinal preferences (as opposed to ordinal) and fractional matchings (as opposed to integral). After observing that, in this cardinal setting, stable…
We study a dynamic model of the relationship between two people where the states depend on the "power" in the relationship. We perform a comprehensive analysis of stability of the system, and determine a set of conditions under which stable…
We study dynamic decentralized two-sided matching in which players may encounter unanticipated experiences. As they become aware of these experiences, they may change their preferences over players on the other side of the market.…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
We present a fascinating model that has lately caught attention among physicists working in complexity related fields. Though it originated from mathematics and later from economics, the model is very enlightening in many aspects that we…
We study the optimization of the stable marriage problem. All individuals attempt to optimize their own satisfaction, subject to mutually conflicting constraints. We find that the stable solutions are generally not the globally best…
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…
In the Stable Roommates Problem (SR), a set of $2n$ agents rank one another in a linear order. The goal is to find a matching that is stable: one that has no pair of agents who mutually prefer each other over their assigned partners. We…
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…
Cooperation through repetition is an important theme in game theory. In this regard, various celebrated ``folk theorems'' have been proposed for repeated games in increasingly more complex environments. There has, however, been insufficient…