Paper:
We propose a multi-agent learning approach for designing crowdsourcing contests and all-pay auctions. Prizes in contests incentivise contestants to expend effort on their entries, with different prize allocations resulting in different incentives and bidding behaviors. In contrast to auctions designed manually by economists, our method searches the possible design space using a simulation of the multi-agent learning process, and can thus handle settings where a game-theoretic equilibrium analysis is not tractable. Our method simulates agent learning in contests and evaluates the utility of the resulting outcome for the auctioneer. Given a large contest design space, we assess through simulation many possible contest designs within the space, and fit a neural network to predict outcomes for previously untested contest designs. Finally, we apply mirror descent to optimize the design so as to achieve more desirable outcomes. Our empirical analysis shows our approach closely matches the optimal outcomes in settings where the equilibrium is known, and can produce high quality designs in settings where the equilibrium strategies are not solvable analytically.

Review:
1. Summary
The authors employ a multi-agent learning approach for learning how to set payoffs optimally for crowdsourcing contests
and auctions. Optimality means e.g. incentive alignment (the principal problem) between the principal (e.g. the organizer) and participants (e.g. bidders), assuming e.g. that participants can be strategic about their behavior. In this work the principal uses ReLU-log utility.
First, the authors use fictitious play and multi-agent RL to train agents on a distribution of payoffs. Then, a neural net is fitted to the samples (payyoffs, expected principal utility), and finally iteratively attempts to improve the payoffs using mirror ascent within the convex set of admissable payoffs.
The authors compare the payoffs with theoretically known solutions and in situations where the optimal solution is not known.
3, 4-agent all-pay auction (Nash eq known).
Same as above, but with noise added to bids (Nash eq not known).
The authors analyze in some detail how the principal's utility and bidder ranking behave as the participants' bids change.
1. Decision (accept or reject) with one or two key reasons for this choice.
Reject. Although the high-level approach is interesting (use learning to design auctions for cases where no theoretical solution is known), the actual experimental results and methodological improvement over e.g. Dutting 2017 are weak. The authors only consider 3, 4-agent auctions. There are no other learned baselines (e.g., constrained optimization without neural nets) that the authors could consider.
3. Supporting arguments
See above.
4. Additional feedback with the aim to improve the paper. Make it clear that these points are here to help, and not necessarily part of your decision assessment.
M-EMA and M-EMD: ascent and descent? in Algo 1, 2?
--- 
I've read the rebuttal, but still lean towards reject. The scope/analysis of the experiments (e.g. auction type), still seems limited, even though both agents and mechanism are adaptive.