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in previous games or during the negotiation process, or an agent may
simply assume his peers to have the same preference as himself. Such
information forms an agent's belief, defined as follows.
Definition 5.2 (Agent Belief in Buyer Coalition Problem)
We define an agent's beliefs
bel
in a buyer coalition problem as fol-
lows. For two agents
i
and
j
, for any two valid bids
b
1
and
b
2
,wesay
bel
i
(
b
1
j
b
2
) if agent
i
believes agent
j
considers
b
1
to be not less
preferred than
b
2
.
Of course, the agents' beliefs, unlike knowledge, are fallible:
bel
i
(
b
1
j
b
2
) does not necessarily imply
b
1
j
b
2
.
In this chapter, we assume each agent's belief is complete in the
sense that for any two agents
i
and
j
, for any two valid bids
b
1
and
b
2
,
we have either
bel
i
(
b
1
j
b
2
)or
bel
i
(
b
2
j
b
1
). In cases where no such
prior knowledge exists, an agent can still maintain a rough estimation
by modelling his fellows' preferences based on his own, or according
to some commonly known principle (e.g., for the same item, a larger
coalition is always more preferable to a smaller one).
5.2.3
NTU Buyer Coalition Games
We are now ready to give a formal model of non-transferable utility
buyer coalition games, and discuss some stability concepts which will
be used as measurement of solution quality of the proposed mecha-
nisms in this chapter. We will first formally define the NTU Games for
buyer coalition problem. After that, we will define the stability con-
cepts of Pareto optimality, the core, and finally, the b-core for buyer
coalition problem.
We first provide a definition for Non-transferable utility buyer coali-
tion games.
Definition 5.3 (NTU-Buyer Games)
An NTU-Buyer game is a
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