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

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 obs...