Population Monotonicity in Matching Games

TL;DR

This paper characterizes when matching games admit population monotonic allocation schemes, providing a clear criterion and an efficient method to determine their existence, advancing cooperative game theory.

Contribution

It offers a necessary and sufficient characterization for the existence of population monotonic schemes in matching games, enabling efficient verification.

Findings

Characterization of when population monotonic schemes exist

Efficient algorithm to determine scheme existence

Theoretical advancement in cooperative game analysis

Abstract

A matching game is a cooperative profit game defined on an edge-weighted graph, where the players are the vertices and the profit of a coalition is the maximum weight of matchings in the subgraph induced by the coalition. A population monotonic allocation scheme is a collection of rules defining how to share the profit among players in each coalition such that every player is better off when the coalition expands. In this paper, we study matching games and provide a necessary and sufficient characterization for the existence of population monotonic allocation schemes. Our characterization also implies that whether a matching game admits population monotonic allocation schemes can be determined efficiently.