Elimination of weakly dominated strategies - example

Question

I am supposed to solve a game by iterated elimination of weakly dominated strategies: $$ \begin{array}{c|c|c|c} & L & C & R \\ \hline T & 2, 1 & 1, 1 & 0, 0 \\ \hline M & 1, 2 & 3, 1 & 2, 1 \\ \hline B & 2, -2 & 1, -1 & -1, -1 \end{array} $$ But I can not find any weakly dominated strategy for any player. $R$ comes close, but $(B, L)$ is worse for player $2$ than $(B, R)$. So, is there any way to approach this?

Answer 1

Step 1: $B$ is weakly dominated by $T$

Step 2: $R$ is weakly dominated by $C$

Step 3: $C$ is weakly dominated by $L$

Step 4: $M$ is weakly dominated by $T$

So the NE you end up with is $(T,L)$. However, remember that iterated elimination of weakly (not strict) dominant strategies can rule out some NE.