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2
Preference Models
2.1
Neoclassical Preference Models
The most prevalent assumption employed by game theory when considering preference
orderings is also the most simple: a preference ordering over alternatives is defined for
each individual agent. Arrow put it succinctly: “It is assumed that each individual in
the community has a definite ordering of all conceivable social states, in terms of their
desirability to him ...It is simply assumed that the individualordersall social states by
whatever standards he deems relevant” [1, p. 17]. According to this view, each agent's
preference ordering is completely defined and immutable before the game begins — it
is categorical. Thus, from the conventional point of view, the starting point of a game is
the definition of categorical utilities for each player. Furthermore, as Friedman argues,
it is not necessary to consider the process by which the agents arrive at their preference
orderings. “The economist has little to say about the formation of wants; this is the
province of the psychologist. The economist's task is to trace the consequences of any
given set of wants” [7, p. 13].
If we take the Arrow/Friedman division of labor as the starting point when defining a
game, we must assume that the individual is able to reconcile all internal conflicts to the
point that a unique categorical preference ordering can be defined that corresponds to its
own self interest and which is not susceptible to change as a result of social interaction.
This is a tall order, but nothing less will do if we are restricted to categorical preference
orderings.
2.2
Social Influence Preference Models
When complex social relationships exist for which categorical preferences are not ade-
quate or appropriate, a natural way for a player to take them into account is by the no-
tion of
influence
. There are many ways to account for social influence, but the approach
presented in this paper is to apply a set of principles to define a systematic and logi-
cally defensible mathematical model that leads to the definition and implementation of
a multiagent decision methodology that accounts for influence relationships when they
exist and treats conventional game theory as a special case when such relationships are
absent.
Principle 1 (Conditioning).
Agents' preferences may be influenced by the preferences
of other agents.
X
j
influences
X
i
if
X
i
's preferences are affected by
X
j
's preferences. Without knowl-
edge of
X
j
's preferences,
X
i
is in a state of suspense with respect to its own prefer-
ences. Essentially,
X
j
's preferences propagate through the group to affect
X
i
's pref-
erences, thereby generating a social bond between the two agents. Once such a bond
exists, it is possible to define a notion of joint preference for the two agents viewed
simultaneously, and it is possible to extract individual preference orderings from this
joint preference ordering since, once
X
j
's preferences are revealed,
X
i
need no longer
remain in suspense. It is thus be possible for both group and individual preferences to
co-exist.
