# Computational Rationalization: The Inverse Equilibrium Problem

arXiv: https://arxiv.org/abs/1308.3506 · HTML: https://mlsanity.com/paper/1308.3506/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2013.

## Built on by (most cited first, 24 of 24)

- [An Algorithmic Perspective on Imitation Learning](https://mlsanity.com/paper/1811.06711/) (2018)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Choice Set Misspecification in Reward Inference](https://mlsanity.com/paper/2101.07691/) (2021)
- [Multi-Agent Imitation Learning: Value is Easy, Regret is Hard](https://mlsanity.com/paper/2406.04219/) (2024)
- [Individual-Level Inverse Reinforcement Learning for Mean Field Games](https://mlsanity.com/paper/2202.06401/) (2022)
- [Multi-agent Inverse Reinforcement Learning for Certain General-sum Stochastic Games](https://mlsanity.com/paper/1806.09795/) (2018)
- [Multi-Agent Advisor Q-Learning](https://mlsanity.com/paper/2111.00345/) (2021)
- [Learning Equilibria from Data: Provably Efficient Multi-Agent Imitation Learning](https://mlsanity.com/paper/2505.17610/) (2025)
- [Equilibrium Inverse Reinforcement Learning for Ride-hailing Vehicle Network](https://mlsanity.com/paper/2102.06854/) (2021)
- [Using Inverse Optimization to Learn Cost Functions in Generalized Nash Games](https://mlsanity.com/paper/2102.12415/) (2021)
- [Auto-Encoding Bayesian Inverse Games](https://mlsanity.com/paper/2402.08902/) (2024)
- [Efficient Inverse Multiagent Learning](https://mlsanity.com/paper/2502.14160/) (2025)
- [Cooperation and Control in Delegation Games](https://mlsanity.com/paper/2402.15821/) (2024)
- [Inverse Concave-Utility Reinforcement Learning is Inverse Game Theory](https://mlsanity.com/paper/2405.19024/) (2024)
- [Deep Incentive Design with Differentiable Equilibrium Blocks](https://mlsanity.com/paper/2603.07705/) (2026)
- [Soft-Bellman Equilibrium in Affine Markov Games: Forward Solutions and Inverse Learning](https://mlsanity.com/paper/2304.00163/) (2023)
- [Operator Splitting for Learning to Predict Equilibria in Convex Games](https://mlsanity.com/paper/2106.00906/) (2021)
- [Learning from Multiple Independent Advisors in Multi-agent Reinforcement Learning](https://mlsanity.com/paper/2301.11153/) (2023)
- [Mean Field Correlated Imitation Learning](https://mlsanity.com/paper/2404.09324/) (2024)
- [Multi-Agent Inverse Q-Learning from Demonstrations](https://mlsanity.com/paper/2503.04679/) (2025)
- [Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games](https://mlsanity.com/paper/2511.05640/) (2025)
- [Bayesian Inverse Games with High-Dimensional Multi-Modal Observations](https://mlsanity.com/paper/2601.00696/) (2026)
- [DIML: Differentiable Inverse Mechanism Learning from Behaviors of Multi-Agent Learning Trajectories](https://mlsanity.com/paper/2601.17678/) (2026)

## Abstract (arXiv)

Modeling the purposeful behavior of imperfect agents from a small number of observations is a challenging task. When restricted to the single-agent decision-theoretic setting, inverse optimal control techniques assume that observed behavior is an approximately optimal solution to an unknown decision problem. These techniques learn a utility function that explains the example behavior and can then be used to accurately predict or imitate future behavior in similar observed or unobserved situations. In this work, we consider similar tasks in competitive and cooperative multi-agent domains. Here, unlike single-agent settings, a player cannot myopically maximize its reward; it must speculate on how the other agents may act to influence the game's outcome. Employing the game-theoretic notion of regret and the principle of maximum entropy, we introduce a technique for predicting and generalizing behavior.