Minimum Cost Stable Outcome in Exchange Networks

One significant problem in exchange networks is finding the equilibrium. To solve this problem, the concept of stable outcome has been developed. However, there are few effective methods to solve it from the point of graph theory. In this paper, we propose a minimum cost stable outcome (MCSO) problem, which is to find a stable outcome whose total transaction cost is minimized. Two algorithms have been designed to solve this problem on unit and general profit networks respectively. For unit profit networks, we use minimum cost edge cover based method to give the optimal solution. For general profit networks, we develop an approximate algorithm and prove that performance ratio is no more than twice the optimal value. Moreover, we provide the probabilistic analysis. At last, extensive experiments have been conducted on synthetic and real-life datasets. Experimental results validate the performance of the proposed algorithms.