NeurIPS 2019
Sun Dec 8th through Sat the 14th, 2019 at Vancouver Convention Center
Paper ID: 1749 Robust Multi-agent Counterfactual Prediction

### Reviewer 1

Update: Based on the authors' response, I am not convinced that my main concerns will be addressed adequately. I will, therefore, maintain my current recommendation. Originality: As far as I know the approach proposed is innovative –– it uses ideas from the partial identification literature, but adapts them to a new setting in a novel way. Quality / Clarity: the paper has a number of issues concerning rigor and clarity. The authors try to explain concepts in words instead of drowning the reader in mathematical formalism –– this is generally a good thing. Unfortunately, this paper falls into the other excess: some important objects are either undefined or defined ambiguously. - What is the mathematical structure of $\mathcal{D}$? What does an element of $\mathcal{D}$ look like? Does it contain information on a single game, or multiple games? Are the types observed and part of $\mathcal{D}$? - On line 132 you have an object $d_i$ that, as far as I can see, is undefined. You call it an action but up to that point actions where denoted $a_i$. You use $d_i$ again when writing down $Regret^{\mathcal{G}}_j$, as if it were an action. - As defined in Definition 1, a utility function takes $N+1$ arguments: N actions and a type (the type coming last). When you use utilities to define the regret, however, the first argument is an action, the second is a type and the third argument, \mathcal{D}_j$is... well, not defined formally anywhere. Please clarify. - You sort of define it in the text but I that the concept of$\epsilon\$-BNE deserved a proper definition environment. - I also found the revelation game somewhat unhelpful for the exposition. I is not clear to me how it connects to problem at hand. Significance: I think that the objective of the paper – relaxing excessively strong assumptions usually made in the literature – is an important one, and any contribution in that direction is welcome.