Understanding Shapley Values with Venn Diagrams

Curated. This was a quite nice introduction. I normally see Shapley values brought up in a context that's already moderately complicated, and having a nice simple explainer is helpful!

I'd like it if the post went into a bit more detail about when/how Shapley values tend to get used in real world contexts.

Do you know whether the person who wrote this would be OK with crossposting the complete content of the article to LW? I would be interested in curating it and sending it out in our 30,000 subscriber curation newsletter, if they were up for it.

This is amazingly clear!

Shapley values are the ONLY way to guarantee: <Efficiency, Symmetry, Linearity, Null player properties>

Well it doesn't end at that: it turns out Shapley values for more than 2 players are not nicely behaved and instead violate Maximin Dominance, as demonstrated in https://www.lesswrong.com/posts/vJ7ggyjuP4u2yHNcP/threat-resistant-bargaining-megapost-introducing-the-rose#ROSE_Value__N_Player_Case__ [LW · GW].

The article I link showed how this is fixed:

Shapley values are about adding everyone one-by-one to a team in a random order and everyone gets their marginal value they contributed to the team.

And that's kinda like giving everyone a random initiative ordering and giving everyone the surplus they can extract in the resulting initiative game.

If we're doing that, then maybe a player, regardless of their position, can ensure they get their maximin value? Maybe this sort of Random-Order Surplus Extraction can work. ROSE.

Explaining the Shapley value in terms of the "synergies" (and the helpful split in the Venn diagram) makes much more intuitive sense than the more complex normal formula without synergies, which is usually just given without motivation. That being said, it requires first computing the synergies, which seems somewhat confusing for more than three players. The article itself doesn't mention the formula for the synergy function, but Wikipedia has it.

I was teaching myself bits of cooperative game theory and this is the clearest explanation I've found so far. I think it's a nice complement to this one [LW · GW].

Thanks, this is a beautiful explanation