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

arXiv 2601.17678 ↗First posted 25 Jan 2026cs.AI cs.GTcited by 0

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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.

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References · 10

  1. 2019Multi-Agent Adversarial Inverse Reinforcement Learningcited by 60
  2. 2017Optimal Auctions through Deep Learning: Advances in Differentiable Economicscited by 38
  3. 2013Computational Rationalization: The Inverse Equilibrium Problemcited by 24
  4. 2023A Scalable Neural Network for DSIC Affine Maximizer Auction Designcited by 23
  5. 2021Adaptive Incentive Design with Multi-Agent Meta-Gradient Reinforcement Learningcited by 18
  6. 2024Contextual Bilevel Reinforcement Learning for Incentive Alignmentcited by 14
  7. 2024Incentivized Learning in Principal-Agent Bandit Gamescited by 13
  8. 2023Multiagent Inverse Reinforcement Learning via Theory of Mind Reasoningcited by 11
  9. 2024On Feasible Rewards in Multi-Agent Inverse Reinforcement Learningcited by 4
  10. 2025Efficient Inverse Multiagent Learningcited by 3

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  1. 2021Multi-Agent Inverse Reinforcement Learning: Suboptimal Demonstrations and Alternative Solution Concepts
  2. 2025Efficient Inference for Inverse Reinforcement Learning and Dynamic Discrete Choice Models
  3. 2018A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress
  4. 2023Discovering Individual Rewards in Collective Behavior through Inverse Multi-Agent Reinforcement Learning
  5. 2025Generalizing Behavior via Inverse Reinforcement Learning with Closed-Form Reward Centroids
  6. 2018Multi-agent Inverse Reinforcement Learning for Certain General-sum Stochastic Games
  7. 2025Multi-Agent Inverse Q-Learning from Demonstrations
  8. 2020Scalable Multi-Agent Inverse Reinforcement Learning via Actor-Attention-Critic