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With these two definitions in place, a possible coalition formation
strategy for the agents as follows.
•
When an agent is invited to join a certain coalition
C
with a conse-
quence
x
, it should accept the invitation if he considers
x
a definite
objection to the current consequence (the consequence that will re-
sult should the agent reject the invitation).
•
On the other hand, if the alternative consequence
x
being offered
by the new coalition is only a potential objection to the current
consequence, then the agent should decide whether to accept it or
not based on some other criteria, such as the risk attitude of that
agent.
Example 3.15
In Example 3.5, the situation of agent
A
1
will be in
the first category if he is currently in a tennis playing coalition, and is
invited to join the grand coalition of all agents to see the new movie
directed by Spielberg. With the evidences
E
=
{
(Director = Spielberg)
∧
(Type = S.F.)
}
,
his own experience
I
1
and preference rules
P
1
, agent
A
1
definitely ob-
jects to
x
1
(all agents playing tennis) using
x
2
(all agents watching
movie). Therefore, he will definitely decide to leave the current coali-
tion and join the new coalition being proposed to him.
Example 3.16
The situation of agent
A
3
in Example 3.5 is in the
second category. The evidences
E
=
{
(Director = Spielberg)
∧
(Type = S.F)
}
leave agent
A
3
in a situation that he cannot decide whether he should
prefer
x
1
-or
x
2
-based only on the evidences. The agent potentially
objects to
x
2
using
x
1
, and it also potentially objects to
x
1
using
x
2
.
Therefore, in real life if agent
A
3
has to make a decision, he must use
some other criteria (such as tossing a coin). However, in the context
of formal analysis as presented in this Chapter, we need to introduce
some new concepts.
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