Information Technology Reference
In-Depth Information
does not hold.
Option 4: No conflicting raisable potential objections.
Alterna-
tively, we can require that for at least one member of the deviating
coalition, the objection does not conflict with his external beliefs.
That is, let
CS
be a coalition structure and let
C
CS
be a
coalition (an objection), we call
C
a raisable objection if there exists
agent
j
in
C
such that for all agent
k
∈
/
C
,neither
∈
k
C
)
B
j
(coal
k
(
CS
)
nor
k
C
)
B
j
(coal
k
(
CS
)
holds.
Before we discuss the above options, we need the following as-
sumption that should be intuitive: if the external belief of an agent is
empty, then in such a case, we expect the agent to behave just as when
external beliefs are not considered in the coalition formation process.
Assumption 6.1
In games where the external beliefs of each agent
is empty (i.e., each agent has no belief whatsoever on the other agents'
preferences), the external belief-based weak core (wb-core), which we
are going to define below, should reduce to the weak core (w-core);
and the external belief-based strong core (which we are going to define
below) should reduce to the strong core (s-core).
This assumption is straightforward enough. If the external belief
of an agent is empty, then in such a case, we expect the agent to
behave just as when external beliefs are not considered in the coalition
formation process.
Now, we can argue that Options 1 and 2 are not preferable by the
following simple argument:
Recall that the external beliefs are not necessarily exhaustive. In
the extreme cases where no external belief exists, this implies that no
objections are raisable if the criteria of Options 1 and 2 is used, and
the consequence of this is that all coalitions will be stable and hence
Search WWH ::
Custom Search