On the existence of stable roommate matchings

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Web1 de set. de 2013 · We propose a new solution concept in the roommate problem, based on the “robustness” of deviations (i.e., blocking coalitions). We call a deviation from a matching robust up to depth k, if none of the deviators gets worse off than at the original matching after any sequence of at most k subsequent deviations. We say that a matching is stable … Web7 de abr. de 2012 · We characterize the computational complexity of checking the existence and computing individual-based stable matchings for the marriage and roommate …

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Web2 de jun. de 2024 · On the existence of stable roommate matchings. Games and Economic Behavior 2000 Journal article DOI: 10.1006/game.1999.0779 EID: 2-s2.0-0347748257. Part of ISSN: 08998256 Contributors: Chung, K.-S. Show more detail. Source: Kim Sau Chung ... WebApplications. Algorithms for finding solutions to the stable marriage problem have applications in a variety of real-world situations, perhaps the best known of these being in the assignment of graduating medical … grass ground clipart

The Roommate Problem Is More Stable Than You Think

Web1 de dez. de 1985 · At least one stable matching exists for every stable marriage instance, and efficient algorithms for finding such a matching are well known. The stable … WebKeywords: Roommate problem, existence, stable matching, cycles JEL: C62, C78 1. Introduction When Gale and Shapley (1962) introduced the roommate problem, they … Web6 de out. de 2005 · Abstract. An instance of the classical Stable Roommates problem (sr) need not admit a stable matching. This motivates the problem of finding a matching that … chittorgarh fort to jodhpur

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On the Existence of Stable Roommate Matchings

Web1 de jul. de 2004 · We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution concept based on the credibility of the deviations for the roommate problem: the bargaining set. We show that weak stability is not sufficient for a matching to be in the bargaining set. WebAlcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May. chittorgarh from delhiWeb1 de set. de 2010 · The aim of this paper is to propose a new solution concept for the roommate problem with strict preferences. We introduce maximum irreversible matchings and consider almost stable matchings (Abraham et al., 2006) and maximum stable matchings (Tan 1990, 1991b). These solution concepts are all core consistent. chittorgarh fort wikipedia

"Weblems all feasible matchings that maximize social surplus are stable. This is not true in roommate problems; but we show how any roommate problem can be \cloned" in order to construct an associated bipartite problem. We then exploit this insight to prove existence of stable matchings in roommate problems with even numbers of agents within each type. " - On the existence of stable roommate matchings

On the existence of stable roommate matchings

Stable Marriage and Roommate Problems with Individual-based …

WebChung, Kim-Sau [2000], "On the Existence of Stable Roommate Matchings," Games and Economic Behavior, 33, 206-230. Simon Clark (2006) "The Uniqueness of Stable Matchings," Contributions to Theoretical Economics: Vol. 6 : Iss. ... Danilov, V.I. [2003]: Existence of stable matchings in some three-sided systems, Mathematical Social … Web1 de jul. de 2004 · We first show that although stable matchings may not exist, a weakly stable matching always exists in a roommate problem. Then, we adopt a solution …

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WebDownloadable! Stable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence of a stable matching is restored when there is an even number of individuals of indistinguishable characteristics and tastes (types). As a consequence, when the number … WebIn stable matching with indifference, some men might be indifferent between two or more women and vice versa. The stable roommates problem is similar to the stable marriage problem, but differs in that all …

WebStable matchings may fail to exist in the roommate matching problem, both when utility is transferable and when it is not. We show that when utility is transferable, the existence … WebAlcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for …

Web3. Restrictions on preferences that admit stable matchings In their paper, Gale and Shapley (1962) speciﬁcally point out that it is not the case that every roommate problem has a stable matching. This has spurred a signiﬁcant amount of re-search aimed at identifying preference restrictions that grant the existence of stable roommate matchings. WebAbstract. The stable roommates problem is that of matching n people into n /2 disjoint pairs so that no two persons, who are not paired together, both prefer each other to their …

Web1 de out. de 2000 · Recently, Chung (1998) has shown that the absence of ‘odd rings’, i.e. rings such that the number of elements is odd, is a sufficient condition for showing the …

Web26 de set. de 2013 · We compare different preference restrictions that ensure the existence of a stable roommate matching. Some of these restrictions are generalized to allow for … grass groomers contract processor grass groomers findlay ohioWeb1 de nov. de 2000 · This paper identifies a condition called “no odd rings” that is sufficient for the existence of stable roommate matchings in the weak preferences case. chittorgarh fort 中文Web1 de mar. de 2024 · We prove that any roommate problem with externalities has a stable partition and that a stable matching exists if there is a stable partition without odd rings. … grass ground farm haileyWebThe set of envy-free matchings turns out to be a lattice, and the set of stable matchings equals the set of fixed points of a Tarski operator on this lattice. Informally speaking, envy-freeness is a relaxation of stability that allows blocking pairs involving a doctor and an empty position of a hospital. grass ground silhouetteWeb3 de nov. de 2024 · Chung K (2000) On the existence of stable roommate matchings. Games Econ Behav 33:206–230. Article Google Scholar Diamantoudi E, Miyagawa E, Xue L (2004) Random paths to stability in the roommate problem. Games Econ Behav 48:18–28. Article Google Scholar grass groomers findlay ohWebcumvent the negative existence and computational complexity results in matching theory. We characterize the computational complexity of checking the existence and computing individual-based stable matchings for the marriage and roommate settings. One of our key computational results for the stable marriage setting also chittorgarh fort was built by