Pareto Optimal Coalitions of Fixed Size

DOI link to open access article: Pareto Optimal Coalitions of Fixed Size

Ágnes Cseh, Tamás Fleiner, Petra Harján

Journal of Mechanism and Institution Design
Volume 4, issue 1, pages 87-108 (November 2019)
doi: 10.22574/jmid.2019.11.003


We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which differ in the size of the rooms to be filled, the orderedness or completeness of the preferences, and the way of calculating the value of a coalition -- based on the best or worst roommate in the coalition. In all cases, we determine the complexity of deciding the existence, and then finding a Pareto optimal assignment, and the complexity of verifying Pareto optimality for a given assignment.

Keywords: Coalition formation, Pareto optimality, complexity.

JEL Classification Numbers: C70, D47.