Stability Under Valuation Updates in Coalition Formation
Abstract
Coalition formation studies how to partition a set of agents into disjoint coalitions under consideration of their preferences. We study the classical objective of stability in a variant of additively separable hedonic games where agents can change their valuations. Our objective is to find a stable partition after each change. To minimize the reconfiguration cost, we search for nearby stable coalition structures. Our focus is on stability concepts based on single-agent deviations. We present a detailed picture of the complexity of finding nearby stable coalition structures in additively separable hedonic games, for both symmetric and non-symmetric valuations. Our results show that the problem is NP-complete for Nash stability, individual stability, contractual Nash stability, and contractual individual stability. We complement these results by presenting polynomial-time algorithms for contractual Nash stability and contractual individual stability under restricted symmetric valuations. Finally, we show that these algorithms guarantee a bounded average distance over long sequences of updates.
Keywords
Cite
@article{arxiv.2602.21041,
title = {Stability Under Valuation Updates in Coalition Formation},
author = {Fabian Frank and Matija Novaković and René Romen},
journal= {arXiv preprint arXiv:2602.21041},
year = {2026}
}