Asymmetric vs incomplete information I am having difficulties in distinguish them. I kind of understand what is the difference intuitively, but I still fail to put some games in the correct category.

Can you give me two examples of games and show me the difference from a mathematical (notation) point of view?
Consider 

where $\epsilon_1,\epsilon_2$ are iid random variables with distribution $F$. $a,b,\dots,h$ are constant parameters.

Game of incomplete but symmetric information
would be something like: $F$ is common knowledge among the two players. 

Game of asymmetric and incomplete information
would be something like: before making their respective decision, Player 1 observes the realization of $\epsilon_1$ but not $\epsilon_2$ and Player 2 observes $\epsilon_2$ but not $\epsilon_1$.