Related papers: Stable matching in a common generalization of the …
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
In the fundamental Stable Marriage and Stable Roommates problems, there are inherent trade-offs between the size and stability of solutions. While in the former problem, a stable matching always exists and can be found efficiently using the…
We consider two-sided matching markets, and study the incentives of agents to circumvent a centralized clearing house by signing binding contracts with one another. It is well-known that if the clearing house implements a stable match and…
Consider the stable matching problem on two sets. We introduce the concept of a preference cycle and show how its natural presence in stable matchings proves a series of classical results in an elementary way.
As AI systems develop in complexity it is becoming increasingly hard to ensure non-discrimination on the basis of protected attributes such as gender, age, and race. Many recent methods have been developed for dealing with this issue as…
Adaptivity to changing environments and constraints is key to success in modern society. We address this by proposing "incrementalized versions" of Stable Marriage and Stable Roommates. That is, we try to answer the following question: for…
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…
Two-sided popular matchings in bipartite graphs are a well-known generalization of stable matchings in the marriage setting, and they are especially relevant when preference lists are incomplete. In this case, the cardinality of a stable…
Although the integration of two-sided matching markets using stable mechanisms generates expected gains from integration, I show that there are worst-case scenarios in which these are negative. The losses from integration can be large…
Are you having trouble getting married? These days, there are lots of products on the market for dating, from apps to websites and matchmakers, but we know a simpler way! That's right -- your path to coupled life isn't through Tinder: it's…
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 study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good…
Motivated by growing evidence of agents' mistakes in strategically simple environments, we propose a solution concept -- robust equilibrium -- that requires only an asymptotically optimal behavior. We use it to study large random matching…
We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose--accept rounds executed by the Gale--Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at…
Consider a one-to-one two-sided matching market with workers on one side and single-position firms on the other, and suppose that the largest individually rational matching contains $n$ pairs. We show that the number of workers employed and…
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.…
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…
Let $G = (A \cup B, E)$ be an instance of the stable marriage problem with strict preference lists. A matching $M$ is popular in $G$ if $M$ does not lose a head-to-head election against any matching where vertices are voters. Every stable…
We study graphs and two-player games in which rewards are assigned to states, and the goal of the players is to satisfy or dissatisfy certain property of the generated outcome, given as a mean payoff property. Since the notion of…
We study the implementability of stable matchings in a two-sided market model with one-sided incomplete information. Firms' types are publicly known, whereas workers' types are private information. A mechanism generates a matching and…