DeepAI AI Chat
Log In Sign Up

Algorithmic Solutions for Maximizing Shareable Costs

by   Rong Zou, et al.
University of Twente
NetEase, Inc

This paper addresses the 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. This means that all subsets of agents have an outside option at a certain cost, and stability requires that the cost shares are defined so that none of the outside options is preferable. 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 paper gives a fairly complete picture of the computational complexity of this optimization problem, in relation to classical computational problems on the core. We also show that, for games with an empty core, the problem is equivalent to computing minimal core relaxations for several relaxations that have been proposed earlier. As an example for a class of cost sharing games with non-empty core, we address minimum cost spanning tree games. While it is known that cost shares in the core can be found efficiently, we show that the computation of maximal cost shares is NP-hard for minimum cost spanning tree games. We also derive a 2-approximation algorithm. Our work opens several directions for future work.


page 1

page 2

page 3

page 4


On the minimum spanning tree problem in imprecise set-up

In this article, we study the Euclidean minimum spanning tree problem in...

The Cost of Stability in Coalitional Games

A key question in cooperative game theory is that of coalitional stabili...

On exact solutions for the minmax regret spanning tree problem

The Minmax Regret Spanning Tree problem is studied in this paper. This i...

The Price of Information in Combinatorial Optimization

Consider a network design application where we wish to lay down a minimu...

Quid Pro Quo allocations in Production-Inventory games

The concept of Owen point, introduced in Guardiola et al. (2009), is an ...

Complexity of Determining Nonemptiness of the Core

Coalition formation is a key problem in automated negotiation among self...

A Study of Proxies for Shapley Allocations of Transport Costs

We propose and evaluate a number of solutions to the problem of calculat...