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will have the motivation to break away, and form a smaller coalition
with Grand-hill Industries to work on the project that bring them $1.5
millions of profit.
There are also other stability criteria proposed for TU games, for
instances, the stable set [5] and the kernel [8], which we will not discuss
because they are out of the scope of this topic. Interested readers may
consult [2] for a good reference on these concepts.
2.3 Coalition Formation Mechanisms
Cooperative game theory deals with the stability of coalitions. So nat-
urally one of its important applications is the analysis of coalition
formation mechanisms (see, for example, [9] for an introduction). In
these works, a coalition formation mechanism is considered to be good
if it can produce many stable results according to some stability con-
cepts such as the core or the kernel. In this section, we will sample some
representative coalition formation approaches, and see what game the-
oretic stability concepts are involved.
One earlier core-based coalition formation approach was proposed
in [10]. In this work the authors proposed an 'two agent auction'-based
mechanism, with the goal of reaching core-stable solutions. Then in
[11], a
propose-and-evaluate
type approach known as KCA was pro-
posed. In this work, each agent starts in its own singleton coalition,
and negotiates in order to form larger coalitions step by step. In each
step, agents make proposals to form new coalitions according to a pay-
off division scheme so that the final outcome will be stable according to
the criterion of the kernel. The proposals are evaluated by other agents,
and if accepted, the corresponding new coalition will be formed.
Another propose-and-evaluate type approach was proposed in [12]
for TU games, where the agents make demands (proposals) in turns.
Unlike [11], however, this one is based on the core, instead of the kernel.
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