Stable partitions in coalitional games

TL;DR

This paper introduces a new concept of stable partitions in coalitional games based on defection functions, analyzing their properties and how they can be reached from initial partitions, with applications to transportation arrangements.

Contribution

It defines and characterizes stable partitions in coalitional games using defection functions, providing a framework for analyzing stability and reachability in such games.

Findings

Characterization of stability for various defection functions

Conditions under which stable partitions can be reached from any initial partition

Application to transportation arrangement optimization

Abstract

We propose a notion of a stable partition in a coalitional game that is parametrized by the concept of a defection function. This function assigns to each partition of the grand coalition a set of different coalition arrangements for a group of defecting players. The alternatives are compared using their social welfare. We characterize the stability of a partition for a number of most natural defection functions and investigate whether and how so defined stable partitions can be reached from any initial partition by means of simple transformations. The approach is illustrated by analyzing an example in which a set of stores seeks an optimal transportation arrangement.