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Pareto optimality in NTU-Buyer games is defined in the conven-
tional way, as follows. Given
n
agents
N
=
{
a
1
,a
2
,...,a
n
}
and a coalition structure
CS
=
{
C
1
,C
2
,...,C
m
}
,
we say
CS
is Pareto optimal if there does not exist another coalition
structure
C
1
,C
2
,...,C
m
}
CS
=
{
such that for each agent
a
∈
N
,wehave
b
a|CS
a
b
a|CS
,
a|CS
a
b
a|CS
for at least one agent.
The second solution concept that we shall define for NTU-Buyer
Games is the core. Traditionally, the core of a coalitional game is a set
of consequences such that, when provided with any of them, an agent
will never be motivated to break away from the grand coalition and
join a smaller coalition for a better consequence (see Definition 2.4).
However, in this Chapter we shall abuse this term and define the core
of an NTU-Buyer game as a stable coalition structure, as follows.
Definition 5.4 (The Core of an NTU-Buyer Game)
Given
n
agents
A
=
{
a
1
,a
2
,...,a
n
}
and a coalition structure
CS
=
{
C
1
,C
2
,...,C
m
}
,
we say
CS
is in the
core of an NTU-buyer game
if there does not exist
another coalition structure
CS
and a subset of agents
C
⊆
A
such
that for each agent
a
∈
C
,wehave
b
a|CS
a
b
a|CS
.
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