Let us consider a prey and a predator. The predator wants to hunt a prey, and it has two choices: either stay Active (search for prey) or Passive (wait for the prey). Similarly, the prey wants to avoid the predator and has same choices as the predator: Active (build a safe zone) or Passive (do nothing for safety). $$\begin{array}{c|cc} & A & P\\ \hline A & 3,-0.8 & 4, -1\\ P & 2,-0.1 & 0,0\end{array}$$ Row is predator, Column is prey.
Are there strictly dominant strategies for the predator or the prey? If yes, what are they (active/passive)? If no, why not?
The strategy $A$ is strictly dominant for the Row player. By playing $A$ versus $B$ he gets $3 > 2$ when Column plays $A$ and $4 > 0$ when Column plays $B$.
Column has no dominant strategies. However, the game is dominance solvable. Once Column knows that $B$ is dominated for Row, Column knows that Row will play $A$ and hence best replies to $A$ by choosing $A$ because $-0.8>-1$. So the unique strategy profile that survives iterated deletion of strictly dominated strategies is $(A,A)$.