Information Architecture and Decision Learnability in Strategic Populations

A coordinator may value groups' outcomes differently but observe only aggregate responses. We study how communication affects its ability to learn an optimal decision in repeated information design with strategic agents. Signals change equilibrium behavior and thereby determine the observation kernels available for learning. We give conditions under which public feedback depends only on pooled composition, while targeted signals provide local identification. Sublinear regret at every population in an observational equivalence class requires a common optimum. In a canonical game, every public learner has linear regret at some member of a fixed pair, whereas one population-independent private policy has at most logarithmic regret at both. Each architecture is compared with its own oracle. A Kullback–Leibler (KL) allocation lower bound accounts for information from optimal play. We compute its canonical value and construct a matching policy, identifying regions with positive and zero logarithmic coefficients. Alternatives approaching a decision boundary instead have local minimax regret of order $\sqrt{T}$. Nonlinear experiments test the induced information geometry: equally costly private probes can differ in whether they resolve a decision, and Gaussian information calculations predict the resulting errors. Adaptive comparisons examine when additional diagnostic sampling improves on greedy decisions.