  We study a network extension to the Nash bargaining game, as introduced by
Kleinberg and Tardos (STOC'08), where the set of players corresponds to
vertices in a graph $G=(V,E)$ and each edge $ij\in E$ represents a possible
deal between players $i$ and $j$. We reformulate the problem as a cooperative
game and study the following question: Given a game with an empty core (i.e. an
unstable game) is it possible, through minimal changes in the underlying
network, to stabilize the game? We show that by removing edges in the network
that belong to a blocking set we can find a stable solution in polynomial time.
This motivates the problem of finding small blocking sets. While it has been
previously shown that finding the smallest blocking set is NP-hard
(Biro,Kern,Paulusma, TAMC'10), we show that it is possible to efficiently find
approximate blocking sets in sparse graphs.
