Comments and Corrections on the DP Equations of Paper "On Team Decision Problems With Nonclassical Information Structures"

The 2023 paper ``On Team Decision Problems With Nonclassical Information Structures'' [1] presented information states and dynamic programming (DP) equations for delayed sharing information patterns, based on the concept of person-by-person (PbP) optimality of static team theory. In particular, [Section IV, 1], Theorem 5 presents recursions of the information states and Theorem 7, eqn(57), eqn(58), presents DP equations, of each team member. In this note we show that the proof of Theorem 5 and the DP eqn(57), eqn(58) of Theorem 7 of [1] are incorrect. Consequently, Lemma 8, Theorem 6, and the full statement of Theorem 7 in [1] are invalid, because their proofs rely on erroneous information states and the optimality of separated strategies (i.e., functions of the information states). We further provide the correct DP equations for PbP optimality, thereby highlighting the subtleties and challenges inherent in the analysis of delayed sharing information patterns.