Understanding Concentrability in Direct Nash Optimization

In this section, we provide detailed theoretical proofs supporting the Direct Nash Optimization (DNO) framework. The proof of Theorem 2 involves a two-step procedure, beginning with regression using logarithmic loss and leading to a squared error bound. The definitions and assumptions draw heavily on concentrability from reinforcement learning theory (specifically the works of Xie et al., 2021, 2023). While the section simplifies some concepts for clarity, a full theoretical analysis is beyond the paper's scope. The proofs also leverage standard results from regression theory, with additional references provided for deeper understanding.