An Integer Programming Approach for Two-Sided Matching with Indifferences

To make use of the collective intelligence of many autonomous self-interested agents, it is important to form a team on which 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 a totally ordered preference list of the agents it is to be paired with, but it is unrealistic to have a totally ordered list for a large-scale two-sided matching problem. In this paper, we propose an integer programming based approach to solve a two-sided matching program that allows indifferences in agents' preferences, and show how an objective function can be defined to find a matching that minimizes the maximum discontentedness of agents in one group.