Non-transferable Utility Games and Coalition Formation Mechanisms - Belief-based Stability in Coalition Formation with Uncertainty - page 18

Mechanisms

2.2 Transferable Utility Cooperative Games

Transferable utility cooperative games (TU games), which are special
cases of NTU games, were first proposed by von Neumann and Mor-
genstern [5]. The idea is that each agent i ∈ N and subset S ⊂ N of
agents in the same coalition can perform some joint action, so that
they, as a group, will receive a real number payoff u ( S )asaresult.
This payoff is known as their utility and can be divided among the
agents in any ways.
We consider an example that illustrate the idea of TU games.

Example 2.3 Three companies, Frankford Corporation, Grand-hill
Industries and Halogen Enterprise discuss to have a joint project. It is
foreseen that the project will bring a profit of $2 millions to the three
companies. In fact, even without Halogen, the other two companies
Frankford and Grand-hill can still take up the project, but the scale
of the project will be reduced, and the anticipated profit will only
be $1.5 millions. Similarly, if less ambitious projects are taken up by
Frankford and Halogen, or Grand-hill and Halogen, or even by any
single company, then the profits of the smaller scale projects will be
less, and different in different situations. Therefore, a di cult problem
is how the profit should be shared by these three companies if they are
to work together for the maximum profit of $2 millions. This is non-
trivial because, for example, if the total profits allocated to Frankford
and Grand-hill is less than $1.5 millions, then these two companies
will have all the reasons to prefer forming a smaller coalition to work
on a smaller scale project, for the profit of $1.5 millions.

We note that in this example the utility is transferable .Thatis,the
utility that a company receives can be transferred, usually in part, to
another company, so as to motivate the latter company to stay in the
coalition. Such an arrangement is generally infeasible in NTU games.
For example, in Example 2.1, a player's utility is generally his or her
degree of 'happiness'. It is just impossible for a player to reduce his or