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The kernel is a solution concept
for a cooperative game. It reflects symmetry properties of the characteristic function
and desirability relations over the set of the players. Given m games over disjoint sets
of players and an m-person game, one defines a compound game over the union of the
m disjoint sets. These m games are the components and the above m-person game is
called the quotient. The quotient may be treated as a game played by representatives
of the component games.
The kernel of the compound game is characterized fully. The compound kernel is,
in fact, a composition of the components’ kernels by means of a distinguished subset
of the imputation space of the quotient game. This subset depends also on the
number of veto players in each component.
An effective formula for the compound kernel is given for compound simple
games. This formula enables short cuts in the computations leading to the kernel of a
decomposable game. The results are applied to compound majority games and a
complete description of their kernels is given.
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