Cooperative games with partial information

Let (N, v) be a cooperative game with transferable utility and $$F\subseteq 2^N$$ F ⊆ 2 N an arbitrary set system, where F represents the set of feasible coalitions S whose worths v(S) are known. We introduce a game $$(N,v_F)$$ ( N , v F ) as follows. If $$S\in F$$ S ∈ F , then $$v_F(S)=v(S)$$ v F ( S ) = v ( S ) and otherwise $$v_F(S)$$ v F ( S ) is defined such that S has zero Harsanyi dividend. By taking different F, this model produces some well-known games directly or indirectly, such as hypergraph games. We characterize the Shapley value of $$(N,v_F)$$ ( N , v F ) on different domains similarly to that for the Myerson value.