The Least-core and Nucleolus of Path Cooperative Games

TL;DR

This paper characterizes the least-core and nucleolus of path cooperative games, showing they are polynomially solvable for network-based scenarios, advancing fair profit distribution methods in multiagent systems.

Contribution

It provides the first polynomial-time algorithms for computing the least-core and nucleolus of path cooperative games based on network flows.

Findings

Characterization of the CS-core, least-core, and nucleolus for path cooperative games.

Polynomial-time algorithms for computing least-core and nucleolus.

Applicability to both directed and undirected networks.

Abstract

Cooperative games provide an appropriate framework for fair and stable profit distribution in multiagent systems. In this paper, we study the algorithmic issues on path cooperative games that arise from the situations where some commodity flows through a network. In these games, a coalition of edges or vertices is successful if it enables a path from the source to the sink in the network, and lose otherwise. Based on dual theory of linear programming and the relationship with flow games, we provide the characterizations on the CS-core, least-core and nucleolus of path cooperative games. Furthermore, we show that the least-core and nucleolus are polynomially solvable for path cooperative games defined on both directed and undirected network.