This paper deals with finding a generalized median stable matching (GMSM), introducedby Teo and Sethuraman (1998) as a fair stable marriage. Cheng (2008) showed that findingthe i-th GMSM is #P-hard in case of i = O(N), where N is the number of stable matchingsof an instance. She also gave an exact algorithm running in polynomial time in case ofi = O(log logN), and the comple...

This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a coalition of vertices is the weight of the maximum size matching in the subgraph induced by the coalition. The Shapley value is one of the most important solution c...

We consider how selfish agents are likely to share revenues derived from maintaining connectivity between important network servers. We model a network where a failure of one node may disrupt communication between other nodes as a cooperative game called the vertex Connectivity Game (CG). In this game, each agent owns a vertex, and controls all the edges going to and from that vertex. A coaliti...

The Banzhaf index, Shapley-Shubik index and other voting power indices measure the importance of a player in a coalitional game. We consider a simple coalitional game called the spanning connectivity game (SCG) based on an undirected, unweighted multigraph, where edges are players. We examine the computational complexity of computing the voting power indices of edges in the SCG. It is shown tha...

This paper studies the complexity of computing solution concepts for a cooperative game, called the minimum base game (MBG) (E; c), where its characteristic function c : 2 E 7! < is de ned as c(S) = (the weight w(B) of a minimum weighted base B S), for a given matroid M = (E;I) and a weight functionw : E 7! <. The minimum base game contains, as a special case, the minimum spanning tree game (MS...