 Definition 3.3  Given that each agent \(k \in N\) has a probability distribution \(\mu_k \in \Delta_k(s_{-k})\), the system of beliefs   \[   \boldsymbol{\mu} = (\mu_1 , \ldots ,\mu_n) \in \Delta_1 (S_{-1}) \times \cdots \times \Delta_n (S_{-n}) \]   is Bayes concordant if and only if,  (3.i) For \(i \ne k, \mu_i (s_{kj}) \gt 0 \Rightarrow s_{kj}\) maximizes \(k\)’s expected utility for some \(\sigma_k \in \Delta_k(s_{-k}),\)   and (3.i) is common knowledge. A pure strategy combination \(\boldsymbol{s} = (s_{1j_1}, \ldots ,s_{nj_n}) \in S\) is rationalizable if and only if the agents have a Bayes concordant system \(\mu\) of beliefs and, for each agent \(k \in N\),  (3.ii) \(E(u_k (s_{kj_k})) \ge E(u_k (s_{ki_k})),\) for \(i_k \ne  j_k\).[24]   