Social Welfare and Pareto Optimality in a Bayesian Game
While it is a bit unusual to describe a strategy profile as being Pareto optimal, especially in the context of Bayesian games, I guess you can still define Pareto optimality in different stages of such games as follows. Recall that in a Bayesian game, a pure strategy is a function $s_i:\Theta_i\to A_i$. 


  A strategy profile $s(\theta)=(s_1(\theta_1),\dots,s_n(\theta_n))$ is
  ex ante Pareto optimal if  \begin{equation} \mathbb E_\theta [u_i(s(\theta);\theta)]\ge \mathbb
 E_\theta[u_i(s'(\theta);\theta)],\quad\text{$\forall i$ and $\forall
 s'(\theta)$} \end{equation} where the above inequality is strict for
  some $i$. [$\mathbb E_\theta$ means taking expectation over the state
  vector $\theta$.]





  A strategy profile $s(\theta)=(s_1(\theta_1),\dots,s_n(\theta_n))$ is
  ex post Pareto optimal if, given a particular realization of states $\bar\theta=(\bar\theta_1,\dots,\bar\theta_n)$, 
  \begin{equation} u_i(s(\bar\theta);\bar\theta)\ge
 u_i(s'(\bar\theta);\bar\theta),\quad\text{$\forall i$ and $\forall
 s'(\bar\theta)$} \end{equation} where the above inequality is strict
  for some $i$.