Improving Quantal Cognitive Hierarchy Model Through Iterative Population Learning

In this paper, we propose to enhance the state-of-the-art quantal cognitive hierarchy (QCH) model with iterative population learning (IPL) to estimate the empirical distribution of agents' reasoning levels and fit human agents' behavioral data. We apply our approach to a real-world dataset from the Swedish lowest unique positive integer (LUPI) game and show that our proposed approach outperforms the theoretical Poisson Nash equilibrium predictions and the QCH approach by 49.8% and 46.6% in Wasserstein distance respectively. Our approach also allows us to explicitly measure an agent's reasoning level distribution, which is not previously possible.