I want to model the situation where there are two players, and they both have two types, they know their own type but not the other's, the only way I can think is to put two "nature" players, but it seems not to be right, so can anyone give me a suggestion about how to model this? I looked through textbooks but were unable to find the answers, please help.
Sorry for lack of details, I looked through the textbooks, the typical type of a game with incomplete information is: the nature choose a state(or the type of, say, player1), and the player 1 knows the type of himself(weak or strong to retaliate the other), player 2 doesn't know player 1's type, but I want to model that: two players know about their own type, but not the other's type, so they are uncertain about doing something bad because they fear the other player has strong power to retaliate.
Assume individual type spaces $T_1 = \{t_1^1, t_2^1 \}$ and $T_2 = \{t_2^1, t_2^2 \}$. The state space is $T = T_1 \times T_2$.
You can visualize $T$ as a $2 \times 2$ matrix: \begin{array}{|c|c|} & t_2^1 & t_2^2 \\ \hline t_1^1 & & \\ \hline t_2^1 & & \\ \hline \end{array}
Now you can represent players' beliefs by means of an ex ante arbitrary probability distribution on the state space $T$. For example: \begin{array}{|c|c|} & t_2^1 & t_2^2 \\ \hline t_1^1 & a & b \\ \hline t_2^1 & c & d \\ \hline \end{array} with $a,b,c,d \ge 0$ and $a+b+c+d = 1$.
Given a type $t_k^i$, player $i$ has belief conditional on his type. For instance, type $t_1^1$ knows his type so his beliefs on the type of 2 (after conditioning on his knowledge) are given by \begin{array}{|c|c|} & t_2^1 & t_2^2 \\ \hline t_1^1 & \frac{a}{a+b} & \frac{b}{a+b} \\ \hline \end{array}