All of midco's Comments + Replies

Analyzing Multiplayer Games using IMPACT

Upon reflection, I now suspect that the Impact  is analogous to Shapley Value. In particular, the post could be reformulated using Shapley values and would attain similar results. I'm not sure whether Impact-scarcity of Shapley values holds, but the examples from the post suggest that it does.

(thanks to TurnTrout for pointing this out!)

Analyzing Multiplayer Games using IMPACT

Answering questions one-by-one:

  • I played fast and loose with IEU in the intro section. I think it can be consistently defined in the Bayesian game sense of "expected utility given your type", where the games in the intro section are interpreted as each player having constant type. In the Bayesian Network section, this is explicitly the definition (in particular, player i's IEU varies as a function of their type).
  • Upon reading the Wiki page, it seems like Shapley value and Impact share a lot of common properties? I'm not sure of any exact relationship, but I'
... (read more)
Generalizing POWER to multi-agent games

We conjecture this? We've only proven limiting cases so far, (constant-sum, and strongly suspected for common-payoff), but we're still working on formulating a more general claim.

2Pattern2moAfter thinking about it more, I don't necessarily see a reason that wouldn't be the case (in theory) for games. My initial reaction was based on considering 'life' as opposed to games, i.e. in a complicated environment new ideas (or ones which require resources or knowledge) might open up more options. (For instance the idea of futures might make an impact, but it seems someone has to think of it, as opposed to it existing as a 'move' in a 'game'.) Of course, dynamics where collaboration increases possible utility, can coexist with dynamics where conflict does, so this might be rare, or require coming up with such ~games* intentionally. *I'm not sure this is a property of games, in theory, though. The world has more 'discovery' going on.
Generalizing POWER to multi-agent games

Thank you so much for the comments! I'm pretty new to the platform (and to EA research in general), so feedback is useful for getting a broader perspective on our work.

To add to TurnTrout's comments about power-scarcity and the CCC, I'd say that the broader vision of the multi-agent formulation is to establish a general notion of power-scarcity as a function of "similarity" between players' reward functions (I mention this in the post's final notes). In this paradigm, the constant-sum case is one limiting case of "general power-scarcity", which I see as th... (read more)

3adamShimi3moGlad to be helpful! I go into more detail in my answer to Alex, but what I want to say here is that I don't feel like you use the power-scarcity idea enough in the post itself. As you said, it's one of three final notes, and without any emphasis on it. So while I agree that the power-scarcity is an important research question, it would be helpful IMO if this post put more emphasis on that connection.