Minimum cost stability in exchange networks

Abstract

Social exchange networks model the behavior of a set of players who need to reach pairwise agreements for making profits. The fundamental problem in exchange networks is how to find the equilibrium such that every participant has no better choices. To resolve this problem, a stable “outcome” which consists of a set of transactions and gains of players in these transactions must be found. In this paper, we first propose the general model of stable outcome applying to arbitrary social graphs, and then present the minimum stability problem (MinSTBL), which is to find the stable outcome the total weight of whose transactions is the minimum. MinSTBL can be employed by governments and companies to stimulate economic participation with the lowest cost. For graphs with unit edge weights, we give an almost optimal solution. For graphs with general edge weights, we prove that the maximum-weight matching is optimal if the graph is bipartite, and propose a relaxed solution that uses at most twice of the optimal cost for regular graphs that are not necessarily bipartite. Our algorithms have been tested on real world social networks and artificial networks, and their effectiveness is evaluated.