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Because of this, we see that it is not su cient to describe such coali-
tions as simply 'stable' (i.e., in the core) or not, as in the classical core-
based approaches. Instead, we propose new stability criteria, the strong
core and the weak core , which classify the obtainable consequences of
a coalition into three stability classes: those that are certainly stable
(the strong core), those that may be stable (the weak core), depending
on the agents' conflict resolution strategy, and those that are certainly
not stable (not in either the strong core or the weak core). We be-
lieve the proposed concepts can provide useful solution concepts for
this type of coalition games, which we called non-transferable utility
games with internal uncertainty .
We shall illustrate these ideas with an elaborated example in Sec-
tion 3.2.
3.2 An Example
In this section we study an example that cannot be handled by the
core-based approaches.
Four agents A 1 to A 4 are planning to do one of two possible activi-
ties: they either go to play tennis or they go to watch a science fiction
(S.F.) movie produced by a director named Steven Spielberg.
To simplify the discussion, suppose the preference of each agent
depends on one factor only, that is, the quality of the movie, which can
be good, average or bad. The agents' exact preferences are described
in Table 3.1. If the movie is good, then all four agents prefer the movie
over tennis. Similarly, if the movie is bad, then all four agents prefer
tennis over movie. However, if the quality is average, then A 1 and A 2 ,
being movie fans, still prefer watching movie, but A 3 and A 4 prefer
playing tennis instead. Also, assuming all else being equal, the agents
prefer to attend an activity in a larger group (i.e., forming a coalition)
to a smaller group. For example, a tennis coalition of four agents is
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