Non-transferable Utility Games and Coalition Formation Mechanisms - Belief-based Stability in Coalition Formation with Uncertainty - page 14

Mechanisms

2.1 Non-transferable Utility Cooperative
Games

The idea of non-transferable utility cooperative games (NTU games)
was first proposed in 1960 by Aumann and Peleg [1]. It was then
re-formulated by later authors including [2]. In latter works, instead
of dealing with the utilities as real numbers, each agent's preference
is represented by a generally partial order on the set of all possible
outcomes, a representation that we will follow.
We first illustrate the basic idea of non-transferable utility cooper-
ative games with an example scenario.

Example 2.1 Consider a group of five people, Alice, Bob, Cindy,
David and Emily. One day they meet in a class reunion party at Bob's
home. After a good meal, they start to discuss how to spend the af-
ternoon. Someone proposes to play contract bridge, another proposes
to play table tennis, while it is also proposed that all of them should
go together to the cinema to see a movie. While they are discussing, it
is soon realised that they do not need to have a universal agreement
on what to do together. It is possible that, say, Alice, Bob, Cindy, and
David play contract bridge for the whole afternoon, while Emily does
whatever she likes by herself, and so on. The complication here is that
everyone of these friends has his or her own preference, and a proposal
is not always going to work (that is, acceptable to everyone involved).
For example, the proposal that Alice, Bob, Cindy, and David play
contract bridge, and Emily goes to see a movie, is not going to work
if David does not particularly like contract bridge, but much prefers
going to see a movie with Emily. Worse, the fact might be that the
three girls Alice, Cindy, and Emily are thinking about leaving the two
boys at home and enjoying shopping by themselves. This is a typical
real life scenario of non-transferable utility cooperative game. We note
that the utility that each one receives as a consequence of realising
a proposal is some kind of 'happiness' associated with the outcome,