Q1: Does Shapley value also works for the non-linear nature of utility within coalition's member?
Q2: What is the maximum possible number of agents can Shapley value be computed?
There are two shortcomings.
1) The Shapley Value may not be an element of the core, supposing the core is non-null, so that it cannot serve as a core assignment algorithm.
2) The Shapley Value assumes additivity, in that the total payoff to two or more games in which the agent participates must be the sum of the payoffs independently. But this seems to exclude games over activities that are complements or substitutes.
I have not been fortunate enough to discuss these matters with Aumann. His views in a 1974 paper seem more cautious, but that paper had little influence in the 20th century and Aumann may have changed his opinions since.
Consider instead the Nucleolus, due to Schmeidler. For a discussion and extension see my book Value Solutions in Cooperative Games.
Both the Shapley Value and the Nucleolus can be computed for any finite number of players.
Q2: The computation of the Shapley-Shubik index for weighted voting games is NP-hard, since it is NP-hard to detect null players. However the power distribution for the International Monetary Fund, consisting of 188 members, can practically be computed in a few minutes, c.f. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2742118
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