Integer Programming Based Stable and Efficiency Algorithm for Two-sided Matching with Indifferences

To make use of collective intelligence of many autonomous self-interested agents, it is important to form a team that all the agents agree. Two-sided matching is one of the basic approaches to form a team that consists of agents from two disjoint agent groups. Traditional two-sided matching assumes that an agent has totally ordered preference list of agents to be paired with. However, it is unrealistic to have a totally ordered list for a large-scale two-sided matching problem. Therefore, two-sided matching with indifferences is proposed. It allows indifferences in the preference list of agents. Two-sided matching with indifferences has two important characters weakly stable and Pareto efficiency. In this paper, we propose a new integer programming based algorithm "nucleolus" for two-sided matching with indifferences. This algorithm propose the matching which satisfies weakly stable and Pareto efficiency.