Irrationality as a mean of regularization in Bayesian Persuasion

We study a regularized variant of the Bayesian Persuasion problem, where the receiver's decision process includes a divergence-based penalty that accounts for deviations from perfect rationality. This modification smooths the underlying optimization landscape and mitigates key theoretical issues, such as measurability and ill-posedness, commonly encountered in the classical formulation. It also enables the use of scalable second-order optimization methods to compute numerically the optimal signaling scheme in a setting known to be NP-hard. We present theoretical results comparing the regularized and original models, including convergence guarantees and structural properties of optimal signaling schemes. Analytical examples and numerical simulations illustrate how this framework accommodates complex environments while remaining tractable and robust. A companion Python library, BASIL, makes use of all the practical insights from this article.