Cooperative games with partial information

摘要

Let (N, v) be a cooperative game with transferable utility and F subset of 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 is an element of 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.