Chapter 12: Bargaining, Weak Dynamics, and Consensus
As with the core for coalition function games, the partition function core may contain more than one partition or, even if only one partition, the core may contain many imputations admissible for that partition. This is well known as a shortcoming of the core, when the core is considered alone as a solution concept; but it is hardly surprising in a stability concept. Stability is a property that may be possessed by a family of states of a system. Nevertheless, given that a partition is stable, we naturally ask how the benefits of that coalition will be distributed among the members. When there is a range of stable imputations, the specific answer to that question is a matter of bargaining. 12.1 BARGAINING In the tradition of game theory, the earliest and best-known discussion of bargaining is that of Nash, for two-person games. Shapley’s value theory has been interpreted as a bargaining theory for n-person games, and it has the advantage that it can always be computed and is always unique. These advantages are shared by Schmeidler’s nucleolus, and the nucleolus has the further advantage that it is within the core, whenever the core is nonnull. Thus the nucleolus can be put to work as a “core-assignment algorithm” – that is, it may be used to determine which of the imputations in the core of a game is hypothetically most likely to occur. For the purposes of this book we adopt the nucleolus in this role. To compute the nucleolus for a...
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