Non-transferable Utility Games and Coalition Formation Mechanisms - Belief-based Stability in Coalition Formation with Uncertainty - page 24

Mechanisms

A word of note: here we describe various coalition formation mech-
anisms using different approaches, based on various game stability con-
cepts. Yet, most of these approaches either have the common knowl-
edge assumptions where private beliefs are not considered, or in the
minority cases where common knowledge are not assumed (e,g., [15,
16]), transferable utility games are considered, and the mechanisms
are not suitable for NTU problems. Still little work have been done
on non-transferable utility games without the common knowledge
assumption.

2.4 Belief and Uncertainties

We end this chapter with a discussion on belief and uncertainties in co-
operative games. While the concepts of Bayesian games are well known
in non-cooperative games, the notion of non-deterministic cooperative
games was not studied until relatively recently. Until the very recent
past, all discussions on both TU and NTU cooperative game theory
concern deterministic games, where the outcome of each coalition is
known for certain, and the utility functions or the preferences of each
fellow agents are assumed to be common knowledge.
However, this assumption is not true in many situations. We can
identify two types of uncertainties in cooperative games. The first is the
uncertainty in regarding the reward or values of the joint actions of the
coalition, namely, the uncertainty of agents' own worth functions. The
second is the uncertainty in the preference of fellow agents: instead
assuming each agent to know for sure the preference (and hence the
outcome of the coalition) of each fellow agent, the agent only has
private beliefs regarding each others. In other words, an agent only
'believe' other agents' worth functions, but does not know other agents'
worth functions for sure.
In transferable utility games, a solution for the first type of uncer-