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The Marxian theory of social class has always been troubled by the fact that the coalitions that individuals form have not, by and large, been consistent with the pattern of asset ownership. The purpose of this paper is to add another dimension to some of the existing approaches to this 'goodness-of-fit' problem. This is done by using n-person game theory to examine the coalitions that individuals would be expected to form in a struggle over division of the surplus. This provides a partial analysis of fragmentation within the working class. [ABSTRACT FROM AUTHOR]