The Cost of Stability in Coalitional Games

07/24/2009
by   Yoram Bachrach, et al.
0

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core--the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable. In this paper, we investigate the possibility of stabilizing a coalitional game by using external payments. We consider a scenario where an external party, which is interested in having the players work together, offers a supplemental payment to the grand coalition (or, more generally, a particular coalition structure). This payment is conditional on players not deviating from their coalition(s). The sum of this payment plus the actual gains of the coalition(s) may then be divided among the agents so as to promote stability. We define the cost of stability (CoS) as the minimal external payment that stabilizes the game. We provide general bounds on the cost of stability in several classes of games, and explore its algorithmic properties. To develop a better intuition for the concepts we introduce, we provide a detailed algorithmic study of the cost of stability in weighted voting games, a simple but expressive class of games which can model decision-making in political bodies, and cooperation in multiagent settings. Finally, we extend our model and results to games with coalition structures.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/27/2023

Human and Machine Intelligence in n-Person Games with Partial Knowledge

In this note, I introduce a new framework called n-person games with par...
research
11/20/2017

Cooperative Games with Bounded Dependency Degree

Cooperative games provide a framework to study cooperation among self-in...
research
06/30/2011

K-Implementation

This paper discusses an interested party who wishes to influence the beh...
research
02/28/2023

Algorithmic Solutions for Maximizing Shareable Costs

This paper addresses the optimization problem to maximize the total cost...
research
02/03/2020

Quid Pro Quo allocations in Production-Inventory games

The concept of Owen point, introduced in Guardiola et al. (2009), is an ...
research
12/11/2021

Stability of Cournot duopoly games with isoelastic demands and quadratic costs

In this discussion draft, we explore different duopoly games of players ...
research
01/08/2023

Geometry of set functions in cooperative game theory

They are many unexplored links between cooperative transferable utility ...

Please sign up or login with your details

Forgot password? Click here to reset