# Shapley value and Mathematica [closed]

I use the TuGames package in Mathematica to analyze cooperative games. Is it possible to calculate Shapley value, Nucleolus, etc., for a large number of players like 400 or more?

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Have you tried? If so, what happens? –  Corey Kelly Jun 9 at 23:18
I use just 3 players like example of package but I think it's difficult for this package to calcul 400 combinations –  Dural Akata Jun 9 at 23:22
You'd need a significant bit of memory since IntegerLength[400!] is "only" 869. –  Artes Jun 9 at 23:24
exactly So it's to hard to see all combinations of coalitions... –  Dural Akata Jun 9 at 23:27
Based on a quick search of "Shapley value algorithm complexity", I find it very unlikely you'll compute it in Mathematica, or by any other means. Computing the value is #P complete, and even linear approximations aren't quick enough for $400!$ interactions. –  Corey Kelly Jun 9 at 23:52