Related papers: Farsighted Collusion in Stable Marriage Problem

We generalize two well-known game-theoretic models by introducing multiple partners matching games, defined by a graph $G=(N,E)$, with an integer vertex capacity function $b$ and an edge weighting $w$. The set $N$ consists of a number of…

We adopt the notion of the farsighted stable set to determine which matchings are stable when agents are farsighted in matching markets with couples. We show that a singleton matching is a farsighted stable set if and only if the matching…

Federated learning is a distributed learning paradigm where multiple agents, each only with access to local data, jointly learn a global model. There has recently been an explosion of research aiming not only to improve the accuracy rates…

Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…

In this paper we consider the issue of a unique prediction in one to one two sided matching markets, as defined by Gale and Shapley (1962), and we prove the following. Theorem. Let P be a one-to-one two-sided matching market and let P be…

We study (coalitional) exchange stability, which Alcalde [Economic Design, 1995] introduced as an alternative solution concept for matching markets involving property rights, such as assigning persons to two-bed rooms. Here, a matching of a…

We consider a learning problem for the stable marriage model under unknown preferences for the left side of the market. We focus on the centralized case, where at each time step, an online platform matches the agents, and obtains a noisy…

To guarantee all agents are matched in general, the classic Deferred Acceptance algorithm needs complete preference lists. In practice, preference lists are short, yet stable matching still works well. This raises two questions: $\bullet$…

Given a set of $n$ men represented by $n$ points lying on a line, and $n$ women represented by $n$ points lying on another parallel line, with each person having a list that ranks some people of opposite gender as his/her acceptable…

It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a…

A recently introduced concept of "cooperative equilibrium", based on the assumption that players have a natural attitude to cooperation, has been proven a powerful tool in predicting human behaviour in social dilemmas. In this paper, we…

Partitioning a large group of employees into teams can prove difficult because unsatisfied employees may want to transfer to other teams. In this case, the team (coalition) formation is unstable and incentivizes deviation from the proposed…

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…

We study the problem of repeated two-sided matching with uncertain preferences (two-sided bandits), and no explicit communication between agents. Recent work has developed algorithms that converge to stable matchings when one side (the…

When computing stable matchings, it is usually assumed that the preferences of the agents in the matching market are fixed. However, in many realistic scenarios, preferences change over time. Consequently, an initially stable matching may…

Many important stable matching problems are known to be NP-hard, even when strong restrictions are placed on the input. In this paper we seek to identify structural properties of instances of stable matching problems which will allow us to…

In the stable marriage problem N men and N women have to be matched by pairs under the constraint that the resulting matching is stable. We study the statistical properties of stable matchings in the large N limit using both numerical and…

Some aspects of the problem of stable marriage are discussed. There are two distinguished marriage plans: the fully transferable case, where money can be transferred between the participants, and the fully non transferable case where each…

In the well-studied Stable Roommates problem, we seek a stable matching of agents into pairs, where no two agents prefer each other over their assigned partners. However, some instances of this problem are unsolvable, lacking any stable…

The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a…