Related papers: Strategic play in stable marriage problem
The set of stable matchings induces a distributive lattice. The supremum of the stable matching lattice is the boy-optimal (girl-pessimal) stable matching and the infimum is the girl-optimal (boy-pessimal) stable matching. The classical…
In 1962, Gale and Shapley \cite{GS} introduced the concept of stable marriages and proved their existence. Since then, the statement of the stability problem has been highly generalized. And a lot of proofs has emerged for the existence in…
The study of marriage dynamics and of strategies to reduce the likelihood of divorce has been an important research area for many years. Gottman's research on successful marriages revealed three matched interaction styles:…
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…
This paper describes the transition of a male-pessimal matching set to optimal when it is a man-oriented approach by deleting a pair from matching set considering the score based approach. A descriptive explanation of the proposed algorithm…
Matching games is a one-to-one two sided market model introduced by Garrido-Lucero and Laraki, in which coupled agents' utilities are endogenously determined as the outcome of a strategic game. They refine the classical pairwise stability…
The standard game-theoretic solution concept, Nash equilibrium, assumes that all players behave rationally. If we follow a Nash equilibrium and opponents are irrational (or follow strategies from a different Nash equilibrium), then we may…
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…
The stable allocation problem is a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is "stable" based…
In this paper, we discuss a stochastic decision problem of optimally selecting the order in which to try $n$ opportunities that may yield an uncertain reward in the future. The motivation came out from pure curiosity, after an informal…
In considering the college admissions problem, almost fifty years ago, Gale and Shapley came up with a simple abstraction based on preferences of students and colleges. They introduced the concept of stability and optimality; and proposed…
We consider the problem of learning stable matchings with unknown preferences in a decentralized and uncoordinated manner, where "decentralized" means that players make decisions individually without the influence of a central platform, and…
In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that…
The Deferred Acceptance (DA) algorithm is an elegant procedure for finding a stable matching in two-sided matching markets. It ensures that no pair of agents prefers each other to their matched partners. In this work, we initiate the study…
The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many…
For most people, social contacts play an integral part in finding a new job. As observed by Granovetter's seminal study, the proportion of jobs obtained through social contacts is usually large compared to those obtained through postings or…
We introduce a new and broader formulation of the stable marriage problem (SMP), called the stable polygamy problem (SPP), where multiple individuals from a larger group $L$ of $|L|$ individuals can be matched with a single individual from…
The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many…
We study the population genetics of Evolution in the important special case of weak selection, in which all fitness values are assumed to be close to one another. We show that in this regime natural selection is tantamount to the…
We present an n-ary constraint for the stable marriage problem. This constraint acts between two sets of integer variables where the domains of those variables represent preferences. Our constraint enforces stability and disallows bigamy.…