# Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games

arXiv: https://arxiv.org/abs/2511.05640 · HTML: https://mlsanity.com/paper/2511.05640/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 36 references that are in the map.
- First posted on arXiv 7 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Provably Efficient Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/1907.05388/) (2019)
- [Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimization](https://mlsanity.com/paper/1603.00448/) (2016)
- [A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progress](https://mlsanity.com/paper/1806.06877/) (2018)
- [Maximum Entropy Deep Inverse Reinforcement Learning](https://mlsanity.com/paper/1507.04888/) (2015)
- [Understanding the impact of entropy on policy optimization](https://mlsanity.com/paper/1811.11214/) (2018)
- [Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization](https://mlsanity.com/paper/2007.06558/) (2020)
- [Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence](https://mlsanity.com/paper/2105.11066/) (2021)
- [Multi-Agent Adversarial Inverse Reinforcement Learning](https://mlsanity.com/paper/1907.13220/) (2019)
- [Identifiability in inverse reinforcement learning](https://mlsanity.com/paper/2106.03498/) (2021)
- [Inverse Optimization: Theory and Applications](https://mlsanity.com/paper/2109.03920/) (2021)
- [Computational Rationalization: The Inverse Equilibrium Problem](https://mlsanity.com/paper/1308.3506/) (2013)
- [Multi-agent Inverse Reinforcement Learning for Two-person Zero-sum Games](https://mlsanity.com/paper/1403.6508/) (2014)
- [Identifiability and generalizability from multiple experts in Inverse Reinforcement Learning](https://mlsanity.com/paper/2209.10974/) (2022)
- [Competitive Multi-agent Inverse Reinforcement Learning with Sub-optimal Demonstrations](https://mlsanity.com/paper/1801.02124/) (2018)
- [Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationality](https://mlsanity.com/paper/2210.01380/) (2022)
- [Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximation](https://mlsanity.com/paper/2009.00162/) (2020)
- [A Robust Utility Learning Framework via Inverse Optimization](https://mlsanity.com/paper/1704.07933/) (2017)

## Abstract (arXiv)

Inverse Game Theory (IGT) methods based on the entropy-regularized Quantal Response Equilibrium (QRE) offer a tractable approach for competitive settings, but critically assume the agents' rationality parameter (temperature τ) is known a priori. When τ is unknown, a fundamental scale ambiguity emerges that couples τ with the reward parameters (θ), making them statistically unidentifiable. We introduce Blind-IGT, the first statistical framework to jointly recover both θ and τ from observed behavior. We analyze this bilinear inverse problem and establish necessary and sufficient conditions for unique identification by introducing a normalization constraint that resolves the scale ambiguity. We propose an efficient Normalized Least Squares (NLS) estimator and prove it achieves the optimal O(N-1/2) convergence rate for joint parameter recovery. When strong identifiability conditions fail, we provide partial identification guarantees through confidence set construction. We extend our framework to Markov games and demonstrate optimal convergence rates with strong empirical performance even when transition dynamics are unknown.