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[2511.05640] Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games
Summary
This paper presents Blind Inverse Game Theory, a novel framework for jointly decoding rewards and rationality in entropy-regularized competitive games, addressing the challenge of unknown rationality parameters.
Why It Matters
The study is significant as it introduces a new statistical framework that resolves the scale ambiguity in Inverse Game Theory, allowing for better parameter recovery in competitive settings. This advancement can enhance the understanding of agent behavior in various applications, including economics and AI.
Key Takeaways
- Introduces Blind-IGT for joint recovery of reward and rationality parameters.
- Addresses scale ambiguity in Inverse Game Theory with a normalization constraint.
- Proposes an efficient Normalized Least Squares estimator with optimal convergence rates.
- Extends the framework to Markov games, demonstrating strong empirical performance.
- Provides partial identification guarantees when strong identifiability conditions fail.
Computer Science > Machine Learning arXiv:2511.05640 (cs) [Submitted on 7 Nov 2025 (v1), last revised 21 Feb 2026 (this version, v2)] Title:Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games Authors:Hamza Virk, Sandro Amaglobeli, Zuhayr Syed View a PDF of the paper titled Blind Inverse Game Theory: Jointly Decoding Rewards and Rationality in Entropy-Regularized Competitive Games, by Hamza Virk and 2 other authors View PDF HTML (experimental) Abstract: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 $\tau$) is known a priori. When $\tau$ is unknown, a fundamental scale ambiguity emerges that couples $\tau$ with the reward parameters ($\theta$), making them statistically unidentifiable. We introduce Blind-IGT, the first statistical framework to jointly recover both $\theta$ and $\tau$ 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 $\mathcal{O}(N^{-1/2})$ convergence rate for joint parameter recovery. When strong identifiability conditions fail, we provide partial identification gua...
