On the Population Monotonicity of Independent Set Games
Libing Wang, Han Xiao, Donglei Du, Dachuan Xu

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.
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