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have been developed, especially in cooperative game theory.
In a non-transferable utility (NTU) game with a set
N
of agents,
each coalition
S
N
is associated with a set
V
(
S
) of consequences,
which are the possible outcomes of the game as a result of the agents'
joint action of forming the coalition
S
. One classic solution concept
in cooperative game theory is the core, which defines that a certain
allocation for a coalition is stable (i.e., in the core) if no individual
members, or groups of members, can defect from the original coali-
tion
S
to obtain a more preferable outcome for each of the defecting
members in
S
. In order to analyse the game for the core, it is required
that the possible consequences
V
(
S
) of each possible coalition
S
(or
its worth
v
(
S
) if the game is a TU game), as well as the agents' pref-
erences, are known for certain. This means that each agent is not only
assumed to know its own preference, but rather, it is assumed to know
the preferences of all other agents, and also how other agents will act
given their preferences, assuming that all agents are rational.
However, in many software agent problems, we are not able to at-
tach such exact possible consequence functions, or worth functions,
and agent preferences, to every coalitional game that we analyse, as
there are often uncertainties regarding the achievable outcomes of a
coalition. After all, software agents are not omniscient, and we cannot
assume that the agents
know
for sure how each other will act accord-
ing to their own
private beliefs
of the possible consequence functions
(or worth functions) and other agents' preferences, even if they are ra-
tional. (Although they can still have
private beliefs
of how each other
will act.)
⊆
Example 3.1
Ivy and Jill are deciding whether to play in the after-
noon. However, the weather is not very good and it might rain in the
afternoon. If it really rains, then both would rather stay at home, as
Ivy just bought a new topic and she is eager to read it, and Jill needs
to vacuum the house before she can travel overseas next week for hol-
idays. However, if it does not rain, then both of them would definitely
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