Visual Representation of mixed strategy profile using a simplex in $R^3$ I am looking for a reference to learn how to plot mixed strategy profile in a two player game with three pure strategies. 

Looking forward to any advice or suggestion.

(Here is the question regarding simplex I posted in mathematics.stackexchange)
I'm not sure what you're asking is possible.

Start with the intuition from the case with 2 pure strategies. A player's mixed strategy is a 2-vector $\sigma_i(p)=(p,1-p)$, which can be visualized on a 1-dimensional simplex (or simply a line). Therefore, a profile of two mixed strategies can be represented as a point in a 2-dimentional plane, because this profile is controlled by two parameters (say $p$ for player 1 and $q$ for player 2) like the following 



With 3 pure strategies, a mixed strategy is a 3-vector $\sigma_i(p_1,p_2)=(p_1,p_2,1-p_1-p_2)$. It is controlled by two parameters, and so we need a 2-dimensional simplex to represent one (mixed) strategy. For a profile of two mixed strategies, we need two 2-dimensional simplices, or planes. Naturally they should be perpendicular to each other just like the two 1-dimensional simplices are in the 1-dimensional case, although this is not a hard requirement. The difficult part is that we now have four controlling parameters, e.g. $p_1,p_2$ for player 1 and $q_1,q_2$ for player 2. So the strategy profile lives in a 4-dimensional space, which is impossible to visualize. 

The following is a failed example. Player 1's mixed strategy $\sigma_1(\hat p_1,\hat p_2)$ lives in the blue simplex and Player 2's mixed strategy $\sigma_2(\hat q_1,\hat q_2)$ lives in the orange simplex. The two simplices share the vertical axis, but this is not necessary. As the two red dashed lines show, it's not always possible to find an "intersection" of the two strategies (the two lines have different heights).