ECONOMY

david austen-smith 901
understanding of coalition structure and provide the first thoroughgoing effort to
apply game theory to understand politics. Cooperative game theory is distinguished
essentially by the presumption that if gains from cooperation or collusion were
available to a group of agents, then those gains would surely be realized. As such,
it is closely tied to the Arrovian approach to preference aggregation and much of
the early work stimulated by Riker’s contribution reflected concerns similar to those
addressed in the possibility theorem. An important concept here is that of the core of
a cooperative game.
Loosely speaking, if an alternative x is in the core, then any coalition of individuals
who agree on a distinct alternative y that they all strictly prefer, cannot be in a position
to replace x with y. For example, the majority rule core contains only alternatives that
cannot be defeated under majority voting. Similarly, if we imagine that a group uses
a supramajority rule requiring at least 2/3 of the group to approve any change, then
x is in the core if there is no alternative y such that at least 2/3 of the group strictly
prefer y to x. So if a group involves nine individuals, five of whom strictly prefer x to
y and the remaining four strictly prefer y to x, then the majority rule core (when the
choice is between x and y)isx alone whereas both x and y are in the 2/3 rule core.
The concept of the core is intuitively appealing as a predictor of what might happen.
Given the actions available to individuals under the rules governing any social
interaction, and assuming that coalitions can freely form and coordinate on mutually
advantageous courses of action, the core describes those outcomes that cannot be
overturned: even if a coalition does not like a particular core outcome, the very fact
that the outcome is in the core means that the coalition is powerless to overturn it.
On the other hand, when the core is empty (that is, fails to contain any alternatives)
then its use as a solution concept for a cooperative game-theoretic model is suspect.
For example, suppose a group of three persons has to use majority rule to decide
how to share a dollar and suppose every individual cares exclusively about their own
share. Then every possible outcome (that is, division of the dollar) can be upset by
amajoritycoalition.Toseethis,supposeafairdivisionof$(1/3) to each individual
is proposed; then individuals (say, A and B) can propose and vote to share the dollar
evenly between themselves and give nothing to individual C; but then A and C can
propose and vote to give $(2/3)toAand$(1/3) to C. Because A and C care only about
their own shares, this proposal upsets the proposal favoring A and B. But by the same
token, a division that shares the dollar equally between C and B, giving nothing to
A, upsets the outcome that gives B nothing; and so on. In this example, the core
offers no guidance about what to expect as a final outcome. Furthermore, it does not
follow that the core being empty implies instability or continued change. Rather, core
emptiness means only that every possible outcome can in principle be overturned; as
such, the model offers no prediction at all. It is an unfortunate fact, therefore, that,
save in constrained environments, the core of any cooperative game-theoretic model
of political behavior is typically empty, attenuating the predictive or explanatory
content of the model.
Discovering the extent to which the core failed to exist was disappointing and induced
at least some pessimism about the general value of formal economic reasoning