The aim of this paper is to propose a new solution for the roommate problem with strict references. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2]) and maximum stable matchings (Tan [30] [32]). We find that almost stable matchings...

Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In...

A matching game is a cooperative game (N; v) defined on a graph G = (N;E) with an edge weighting w : E ! R+. The player set is N and the value of a coalition S N is dened as the maximum weight of a matching in the subgraph induced by S. First we present an O(nm+n2 log n) algorithm that tests if...

The stable roommates problem with payments has as input a graph G(E,V) with an edge weighting w:E_ùR+ and the problem is to find a stable solution. A solution is a matching M with a vector p.RV that satisfies pu+pv=w(uv) for all uv.M and pu=0 for all u unmatched in M. A solution is stable if it...

In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have...

Scarf's algorithm [18] provides fractional core elements for NTU-games. Bir¢ and Fleiner [3] showed that Scarf's algorithm can be extended for capacitated NTU-games. In this setting agents can be involved in more than one coalition at a time, cooperations may be performed with different...

Local routing protocols in scale free networks have been extensively studied. In this paper we consider a wireless contextualization of this routing problem and analyze on the one hand how cooperation affects network efficiency, and on the other hand the stability of cooperation structures....

We consider various lexicographic allocation procedures for coalitional games with transferable utility where the payoffs are computed in an externally given order of the players. The common feature of the methods is that if the allocation is in the core, it is an extreme point of the core. We...

In finance risk capital allocation raises important questions both from theoretical and practical points of view. How to share risk of a portfolio among its subportfolios? How to reserve capital in order to hedge existing risk and how to assign this to different business units? We use an...

There lies a network structure between fixed tree and minimum cost spanning tree networks that has not been previously analyzed from a cooperative game theoretic perspective, namely, directed acyclic graph (DAG) networks. In this paper we consider the cost allocation game defined on...