The game-table is given below
$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$ $G = \begin{bmatrix} (5,2) & (3,1) \\ (3,5) & (\delta, 5)\\ (1,2) & (5,1) \end{bmatrix} $
It is quickly established that no pure strategies is strictly dominating. $\delta$ is unknown with $\delta$ $\in$ $\mathbb{R}$, so there is a basis for elimination of weakly dominating strategies.
How would we proceed from here?
- For $\delta > 5$ its clear that $E[u(R2)]>E[u(R3]$ $\forall$ p.
However, this doesn't hold for the assumption made. And we are back to start.
Solving for $p$ with inequality between $E[u(R2)]>E[u(R3]$ we are restricting $\delta$ which goes against the assumption.
And likewise when solving for $\delta$.
Check the definition of what it means for a strategy to be weakly dominated by another strategy.
Say the strategies for Player 1 and 2 are $A=\{a_1,a_2,a_3\}$ and $B=\{b_1,b_2\}$ respectively. You'll find that $b_1$ weakly dominates $b_2$, so we may eliminate $b_2$. Then $a_1$ strictly (and therefore weakly) dominates $a_2$ and $a_3$, so we may eliminate those two.
Then $(a_1,b_1)$ is the only remaining strategy, which we obtain without knowledge of $\delta$.