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.
Shapley, Lloyd S., On Balanced Sets and Cores. Santa Monica, CA: RAND Corporation, 1965. https://www.rand.org/pubs/research_memoranda/RM4601.html. Also available in print form.
Shapley, Lloyd S., On Balanced Sets and Cores, Santa Monica, Calif.: RAND Corporation, RM-4601-PR, 1965. As of September 09, 2021: https://www.rand.org/pubs/research_memoranda/RM4601.html