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Zerosum games. A coailitional game with transferable payoff is zerosum if $v(S) + v(N - S) = v(N)$ for every coalition $S$; it is additive if $v(S) + v(T) = v(S \cup T)$ for all disjoint $S$ and $T$. Show that a zerosum game that is not additive has an empty core.

I'm unsure how to approach this proof? Any help would be appreciated

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