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the only) relevant rationality notion in mixed-motive environments, such as those that
contain opportunities for cooperation, compromise, and unselfishness. Arrow clearly
delimits the context in which individual rationality applies: “[R]ationality in application
is not merely a property of the individual. Its useful and powerful implications derive
from the conjunction of individual rationality and other basic concepts of neoclassical
theory — equilibrium, competition, and completeness of markets ...When these as-
sumptions fail, the very concept of rationality becomes threatened, because perceptions
of others and, in particular, their rationality become part of one's own rationality” [2,
p. 203].
Despite Arrow's caution, the mathematical and logical structures of game theory
are routinely applied to mixed-motive situations, often producing results that are at
variance with observed behavior. Behavioral economics (e.g., see [3]) seeks to mitigate
this problem by inserting parameters to model fairness, loss aversion, and other such
issues into the utilities to provide more psychological realism. Once included, however,
the game is still solved according to conventional individual rationality and categorical
utilities.
What is missing with conventional game theory is a notion of group benefit. Co-
operative multiagent systems are designed such that the individuals work together to
accomplish some task, but, unfortunately, group rationality does not derive from indi-
vidual rationality. As observed by Luce and Raiffa, “the notion of group rationality is
neither a postulate of the model nor does it appear to follow as a logical consequence
of individual rationality ...general game theory seems to be in part a sociological the-
ory which does not include any sociological assumptions ...it may be too much to ask
that any sociology be derived from the single assumption of individual rationality” [10,
p. 193, 196]. Consequently, game theory has proceeded by making assumptions about
individual preferences only and then using those preferences to deduce information
about the choices (but not the values) of a group.
It might be expected that cooperative game theory possesses some notion of group
rationality. This version of game theory permits a subset of players to enter into a coali-
tion such that each receives a payoff that is greater than it would receive if it acted
alone. However, cooperative game theory employs categorical utilities and its solutions
concepts are based squarely upon the assumption of individual rationality. Each player
enters into a coalition solely on the basis of benefit to itself and, even though each may
be better off for having joined, a notion of group rationality is not an issue when forming
the coalition.
Reliance on categorical utilities and individual rationality limits the application of
conventional game theory for the design and synthesis of multiagent systems that are
intended to be cooperative. The contributions of this paper are (i) to present a new
utility structure that overcomes the limitations of categorical utilities as a model of
complex social relationships, (ii) to offer a more general concept of rational behavior
that simultaneously accounts for both group an individual welfare, and (iii) to address
and control the computational complexity of the resulting model.
