learning process converges in polynomial time to the core.  While convergence to the core is known for some types of … random walks and matching theory. …

In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core … interpretation of these results for matching games. Finally we consider an even more general setting where players' contributions in … in many practical applications, such as NRMP (National Resident Matching Program). …

) blocking dynamics in two-sided one-to-one matching markets with continuous side payments (assignment problems, Shapley and … obtained from the previous one by satisfying a blocking pair (i.e., by matching the two blocking agents and assigning new … the model (i.e., for marriage markets, one-to-one matching, or discretized assignment problems), the existence of blocking …

. First we present an O(nm+n2 log n) algorithm that tests if the core of a matching game defined on a weighted graph with n … with payments. Second we show that the nucleolus of an n-player matching game with a nonempty core can be computed in O(n4 …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 …

v with pu+pv<w(uv). By pinpointing a relationship to the accessibility of the coalition structure core of matching games … 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 … blocking value, respectively, are NP-complete. Finally, we prove that the first problem is NP-complete also when a matching is …