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A Conditional Game-Theoretic Approach
to Cooperative Multiagent Systems Design
Wynn Stirling
Electrical and Computer Engineering Department, Brigham Young University
Provo, Utah 84602, U.S.A.
Abstract.
Neoclassical game theory focuses exclusively on individual prefer-
ences, which are more naturally attuned to competitive, rather than cooperative,
decision scenarios. Conditional game theory differs from classical theory in two
fundamental ways. First, it involves a utility structure that permits agents to de-
fine their preferences conditioned on the preferences of other agents, and second,
it accommodates a notion of group rationality as well as individual rationality.
The resulting framework permits a notion of group preferences to be defined, and
permits solution concepts that account for both individual and group interests.
Keywords:
Group Rationality, Cooperation, Negotiation.
1
Introduction
Game theory provides a mathematical framework within which to model decisions by
multiple entities where the outcome for each depends on the choices of all. Game the-
ory is increasingly invoked by engineering and computer science as a framework for
multiagent systems [11,12,15,17,18].
A finite, noncooperative, single-stage, strategic-form game consists of (i) a set of
autonomous decision makers, or
players
, denoted
X
n
=
{X
1
,...,X
n
}
where
n ≥
2
,
(ii) a finite action set
A
i
for each
X
i
, and (iii) a
utility
u
X
i
:
AA→
R
for each
X
i
,
i
=1
,...,n
,where
A
=
A
1
×···×A
n
is the product action space. For any
action
profile
a
=(
a
1
,...,a
n
)
, the utility
u
X
i
(
a
)
, defines the benefit to
X
i
as a conse-
quence of the instantiation of
a
. These utilities are
categorical
in the sense that
u
X
i
(
a
)
unconditionally defines the benefit to
X
i
of the group instantiating the action profile
a
.
X
i
also must possess a logical structure that defines how it should play the game. The
most widely used logical structure is the doctrine of
individual rationality
:
each
X
i
should act in a way that maximizes is own utility. Under the assumption that
each player subscribes to this notion and assumes that all others do so as well, they each
will solve their corresponding constrained optimization problem, resulting in a Nash
equilibrium.
These mathematical and logical structures may provide an appropriate vehicle with
which to model behavior in an environment of competition and market driven expec-
tations since, in that environment, the dominant notion of rational behavior clearly is
self-interest. It is less clear, however, that self-interest is the dominant (and certainly not
∈A
