Cooperative games with partial information

Let ( N , v ) be a cooperative game with transferable utility and 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 ) as follows. If S ∈ F , then v F ( S ) = v ( S ) and otherwise 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 ) on different domains similarly to that for the Myerson value.