I think a general and theoretically sound approach would be to build a single composite game to represent all of the games together
Yeah, I did actually have this thought but I guess I turned it around and thought: shouldn’t an adequate notion of value be invariant to how I decide to split up my games? The linearity property on Wikipedia even seems to be inviting us to just split games up in however manner we want.
And yeah, I agree that in the real world games will overlap and so there will be double counting going on by splitting games up. But if that’s all that’s saving us from reaching absurd conclusions then I feel like there ought to be some refinement of the Shapley value concept...
Yeah, I did actually have this thought but I guess I turned it around and thought: shouldn’t an adequate notion of value be invariant to how I decide to split up my games? The linearity property on Wikipedia even seems to be inviting us to just split games up in however manner we want.
And yeah, I agree that in the real world games will overlap and so there will be double counting going on by splitting games up. But if that’s all that’s saving us from reaching absurd conclusions then I feel like there ought to be some refinement of the Shapley value concept...