reviews: 
Comments: The paper introduces a generative-adversarial (or min-max) characterization of the inverse game theory problem where a generator provides payoff parameters that minimize total regret, and a discriminator looks for action-profiles that maximize it. A min-max objective mimicking this two-player game is optimized to estimate the inverse equilibrium using gradient descent ascent algorithm (and other variations of it). It is further proposed that for games that satisfy certain assumptions guaranteeing convex-concavity of the objective, the algorithm converges in a number of iterations that are polynomial in the precision of the obtained inverse equilibrium. This formulation is further extended to give algorithms for multi-agent inverse reinforcement learning and multi-agent apprenticeship learning, accompanied by polynomial time (and space) convergence guarantees under appropriate assumptions. Experiments are conducted to identify categories of games for which the method is effective, and whether its usefulness goes beyond provided theoretical limits.
Strengths: * An inverse game theoretic perspective to multi-agent inverse reinforcement learning is certainly a novel direction to approach the problem with. Backed by results in inverse game theory, this approach leads to algorithms with desirable convergence guarantees that prior work in multi-agent imitation learning does not provide.

* The low restrictiveness of the assumptions made allow for the framework to be effective on a vast majority of markov games, leading to useful and efficient solutions on a wide variety of multi-agent problems.

* While the paper focuses on the inverse nash equilibrium, the simplicity of the objective allows for easy extensions of the framework to alternative game theory solution concepts.

* All presented algorithms are succinct and easy to understand. Sufficient mathematical background is provided as and when necessary.
Weaknesses: * It would be helpful to expand on the proofs of theorems 6.1, 6.2, and 6.3 in the supplementary material. I know that a reference has been provided, but a slight explanation of the cited result and how it relates to the theorem in question would be nice.

* Although a comparison of the method has been shown with the ARIMA model on the spanish electricity market data, it would be beneficial to have a comparison with prior methods in inverse multi-agent reinforcement learning. Especially in terms of efficiency since it's one of the main points of the paper. The abstract says that the method outperforms other widely-used methods (plural), and we only get to see it being compared with one other model which is specific to time-series data. 

* Some comparison/contextualization with prior work in multiagent inverse reinforcement learning would also be helpful.
Recommendation: 6: marginally above the acceptance threshold
Reviewer confidence: 2: You are willing to defend your assessment, but it is quite likely that you did not understand the central parts of the submission or that you are unfamiliar with some pieces of related work. Math/other details were not carefully checked.
Soundness/correctness: 2 fair
Clarity: 2 fair