On the Population Monotonicity of Independent Set Games

TL;DR

This paper characterizes when independent set cooperative games admit population monotonic allocation schemes, providing a necessary and sufficient condition that can be efficiently verified, advancing fair profit-sharing methods in graph-based problems.

Contribution

It offers a complete characterization of population monotonicity in independent set games, including an efficient verification method, which was previously unknown.

Findings

Characterization of population monotonic schemes in independent set games

Efficient verification algorithm for the characterization

Enhanced understanding of fair profit-sharing in graph-based cooperative games

Abstract

An independent set game is a cooperative game defined on graphs and dealing with profit-sharing in maximum independent set problems. A population monotonic allocation scheme is a rule specifying how to share the profit of each coalition among its participants such that every participant is better off when the coalition expands. In this paper, we provide a necessary and sufficient characterization for population monotonic allocation schemes in independent set games. Moreover, our characterization can be verified efficiently.