# DIML: Differentiable Inverse Mechanism Learning from Behaviors of Multi-Agent Learning Trajectories

arXiv: https://arxiv.org/abs/2601.17678 · HTML: https://mlsanity.com/paper/2601.17678/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 13 references that are in the map.
- First posted on arXiv 25 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Optimal Auctions through Deep Learning: Advances in Differentiable Economics](https://mlsanity.com/paper/1706.03459/) (2017)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [A Scalable Neural Network for DSIC Affine Maximizer Auction Design](https://mlsanity.com/paper/2305.12162/) (2023)
- [Adaptive Incentive Design with Multi-Agent Meta-Gradient Reinforcement Learning](https://mlsanity.com/paper/2112.10859/) (2021)
- [Contextual Bilevel Reinforcement Learning for Incentive Alignment](https://mlsanity.com/paper/2406.01575/) (2024)
- [Incentivized Learning in Principal-Agent Bandit Games](https://mlsanity.com/paper/2403.03811/) (2024)
- [Multiagent Inverse Reinforcement Learning via Theory of Mind Reasoning](https://mlsanity.com/paper/2302.10238/) (2023)
- [On Feasible Rewards in Multi-Agent Inverse Reinforcement Learning](https://mlsanity.com/paper/2411.15046/) (2024)
- [Efficient Inverse Multiagent Learning](https://mlsanity.com/paper/2502.14160/) (2025)

## Abstract (arXiv)

We study inverse mechanism learning: recovering an unknown incentive-generating mechanism from observed strategic interaction traces of self-interested learning agents. Unlike inverse game theory and multi-agent inverse reinforcement learning, which typically infer utility/reward parameters inside a structured mechanism, our target includes unstructured mechanism -- a (possibly neural) mapping from joint actions to per-agent payoffs. Unlike differentiable mechanism design, which optimizes mechanisms forward, we infer mechanisms from behavior in an observational setting. We propose DIML, a likelihood-based framework that differentiates through a model of multi-agent learning dynamics and uses the candidate mechanism to generate counterfactual payoffs needed to predict observed actions. We establish identifiability of payoff differences under a conditional logit response model and prove statistical consistency of maximum likelihood estimation under standard regularity conditions. We evaluate DIML with simulated interactions of learning agents across unstructured neural mechanisms, congestion tolling, public goods subsidies, and large-scale anonymous games. DIML reliably recovers identifiable incentive differences and supports counterfactual prediction, where its performance rivals tabular enumeration oracle in small environments and its convergence scales to large, hundred-participant environments. Code to reproduce our experiments is open-sourced.