[Question] What are some alternatives to Shapley values which drop additivity?

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I originally asked this on math.stackexchange; after reading Diffractor’s Unifying Bargaining sequence (Part 1 here) I’m wondering if there are more insights floating about, so I’m repeating it here.

Shapley values seem to be the standard answer to “how should a coalition split the rewards of their cooperation”, but I’m curious about alternatives.

The standard characterization of Shapley values says that Shapley values are the unique coalition payments which satisfy a bunch of properties. Three of them (efficiency, symmetry, and null player) seem pretty necessary for any “reasonable” or “practical” coalition payment rule, but the last one (linearity) does not.

If I didn’t care for linearity (or its close synonyms, additivity and aggregation):

  • What sorts of payment rules become available?

  • What other properties of Shapley values are maintained?

  • What other properties would produce a uniquely characterized payment rule?

Alternatively, are any of the other properties also reasonable to drop (for instance, symmetry)? What do you end up with?

No answers.