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A recursive sequence of sums of consecutive embedded coalitions
Date Issued
2016
ISSN
1312-8876
Citation
International Journal of Mathematical Analysis, 2016, vol. 10(1), pp. 9-14.
Description
Open Access
Type
Peer Reviewed Journal Article
Abstract
The set of players in a cooperative game may be divided into various coalitions forming partitions with different coalition structures. The well-known Bell (1934) number is used to obtain the number of partitions in a n-person cooperative game. The number of embedded coalitions in a partition is the number of subsets formed in that partition. The total number of embedded coalitions in a n-person game is the sum of the numbers of embedded coalitions in different partitions of the game. This article presents a recursive sequence yielding the total sum of the embedded coalitions from a 1-person game to a n-person game.
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