Algorithmic solutions for maximizing shareable costs

This article addresses the linear optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shar...

Full description

Saved in:
Bibliographic Details
Published in:Networks Vol. 84; no. 4; pp. 385 - 397
Main Authors: Zou, Rong, Lin, Boyue, Uetz, Marc, Walter, Matthias
Format: Journal Article
Language:English
Published: Hoboken, USA John Wiley & Sons, Inc 01.12.2024
Wiley Subscription Services, Inc
Subjects:
Algorithms
computational complexity
Constraints
Cost function
cost sharing
Costs
Game theory
Games
Graph theory
Maximization
Minimum cost
minimum spanning tree game
Optimization
ISSN:0028-3045, 1097-0037
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article addresses the linear optimization problem to maximize the total costs that can be shared among a group of agents, while maintaining stability in the sense of the core constraints of a cooperative transferable utility game, or TU game. When maximizing total shareable costs, the cost shares must satisfy all constraints that define the core of a TU game, except for being budget balanced. The article first gives a fairly complete picture of the computational complexity of this optimization problem, its relation to optimization over the core itself, and its equivalence to other, minimal core relaxations that have been proposed earlier. We then address minimum cost spanning tree (MST) games as an example for a class of cost sharing games with non‐empty core. While submodular cost functions yield efficient algorithms to maximize shareable costs, MST games have cost functions that are subadditive, but generally not submodular. Nevertheless, it is well known that cost shares in the core of MST games can be found efficiently. In contrast, we show that the maximization of shareable costs is NP$$ \mathsf{NP} $$‐hard for MST games and derive a 2‐approximation algorithm. Our work opens several directions for future research.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0028-3045
1097-0037
DOI:10.1002/net.22240