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

arXiv 2511.05640 ↗First posted 7 Nov 2025cs.LG cs.GT stat.MLcited by 0

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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.

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

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References · 18

  1. 2018Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actorcited by 4,635
  2. 2019Provably Efficient Reinforcement Learning with Linear Function Approximationcited by 514
  3. 2016Guided Cost Learning: Deep Inverse Optimal Control via Policy Optimizationcited by 400
  4. 2018A Survey of Inverse Reinforcement Learning: Challenges, Methods and Progresscited by 294
  5. 2015Maximum Entropy Deep Inverse Reinforcement Learningcited by 173
  6. 2018Understanding the impact of entropy on policy optimizationcited by 171
  7. 2020Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularizationcited by 170
  8. 2021Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergencecited by 83
  9. 2019Multi-Agent Adversarial Inverse Reinforcement Learningcited by 60
  10. 2021Identifiability in inverse reinforcement learningcited by 55
  11. 2021Inverse Optimization: Theory and Applicationscited by 48
  12. 2013Computational Rationalization: The Inverse Equilibrium Problemcited by 24
6 more
  1. 2014Multi-agent Inverse Reinforcement Learning for Two-person Zero-sum Gamescited by 17
  2. 2022Identifiability and generalizability from multiple experts in Inverse Reinforcement Learningcited by 16
  3. 2018Competitive Multi-agent Inverse Reinforcement Learning with Sub-optimal Demonstrationscited by 11
  4. 2022Inverse Game Theory for Stackelberg Games: the Blessing of Bounded Rationalitycited by 5
  5. 2020Learning Nash Equilibria in Zero-Sum Stochastic Games via Entropy-Regularized Policy Approximationcited by 4
  6. 2017A Robust Utility Learning Framework via Inverse Optimizationcited by 3

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