Information Technology Reference
In-Depth Information
Mechanisms
Some early solution concepts had already been well known in eco-
nomics circles before the emergence of game theory. One of them is
the
individual rationality
(IR) concept, which requires every cooperat-
ing agent to be able to gain no less than the utility that he can obtain
by not cooperating. That is, no agent is to be worse off by cooper-
ating, than not cooperating and forming its own singleton coalition.
For instance, in the scenario of Alice, Bob, Cindy, David, and Emily,
which we have just considered, individual rationality refers to the con-
dition that each of these five people is more willing to participate in
the game, hoping for an outcome better than simply leaving Bob's
home and being alone.
Definition 2.2 (Individual Rationality in NTU Games)
A
non-transferable utility game (NTU game)
g
=
N,X,V,
(
i
)
is
individually rational
if and only if there exists one or more conse-
quences
x
∈
V
(
N
), such that for all agents
i
∈
N
,
x
i
y
for any
consequence
y
∈
V
(
{
i
}
). Such consequences are known as
individually
rational
consequences.
Another early known stability concept is Pareto Optimality (a.k.a.
Pareto E
ciency), proposed by [3]. The idea here is that a coalition
is stable if it has outcome(s), in which it is not possible for any agent
to gain in utility without sacrificing as least one of his fellow agents.
For example, David can increase his utility by forming a coalition with
Emily to see a movie. However, such a move would immediately de-
crease the utilities of Alice, Bob, and Cindy because they can no long
play contract bridge. If there is such an outcome, in which no one can
increase his or her utility without lowering the utility of other per-
son(s), then such an outcome is said to be Pareto optimal. In modern
game theoretic terms, this concept can be defined as follows.
Definition 2.3 (Pareto Optimality in NTU Games)
Anon-
Search WWH ::
Custom Search