Cover: On Balanced Sets and Cores

On Balanced Sets and Cores

Published 1965

by Lloyd S. Shapley


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One of a series of mathematical notes on topics in the theory of multi-person games. This Memorandum establishes a direct correspondence between the balanced sets of coalitions of a multi-person game and the conditions that determine whether the game has a core. A balanced set is a collection of subsets of a finite set that can be so weighted as to cover the whole set uniformly. The core of a game is the set of outcomes that cannot be blocked by a coalition.

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