The Pre Kernel As A Tractable Solution For Cooperative Games PDF Download

A study of the kernel of a cooperative game. In this paper the authors derive a procedure for the players which, if abided by, leads to an outcome in the kernel. Moreover, each outcome in the kernel can be reached by this procedure. The procedure consists of a set of three rules and involves the formation of 'intermediate coalitions' which play 'intermediate games, ' after which the members of each intermediate coalition play a 'reduced game' to decide the share of their spoils. The procedure is further analyzed in the case of monotonic games and in the case of simple games, and the results that are obtained reduce considerably the amount of computation which is needed to compute the kernels of such games. In particular, they compute the kernel of the 7-person projective game (for the grand coalition), which is a star consisting of seven straight-line segments connecting the center to the points of the main simple solution. Finally, conditions under which modifications of the characteristic function do not change its kernel are presented. (Author).