This is the strategic form for a zero-sum game; it reflects player 1's expectations. I need to reduce this strategic form from 4x4 to 2x2 by eliminating the dominated strategies. All the examples I've seen use numbers and I'm struggling in this general case without knowing what a and b are. I've painted grey the strategies I think are dominated. Can someone confirm or deny this result and explain to me the method for computing this?
here's another go at it.
For player 1, $S_{2}$ weakly dominates $S_{4}$ since $a$ and $b$ strictly positive imply $\frac{b}{4}>0$, $0\geq0$, $\frac{a+b}{4}>0$ and $\frac{a}{4}>0$. Similarly, $S_{1}$ weakly dominates $S_{3}$. This leaves only two surviving actions for player 1: $S_{1}$ and $S_{2}$.
Next, (as you mentioned) for player 2, $S_{2}$ strictly dominates $S_{3}$ since $\frac{b-a}{4}>\frac{-(3a+b)}{4}$ and $0>\frac{-(a+b)}{4}$. $S_{2}$ also dominates $S_{4}$ since $\frac{b-a}{4}>-a$ and $0>\frac{-a}{4}$
Maybe I'm still missing something?