Game Theory : Finding Nash equilibrium (non-cooperating)

Question

Consider the game bimatrix

\begin{bmatrix} (1,5) & (3,1) \\ (4,2) & (2,3) \\ (0.3) & (5,2) \end{bmatrix}

It there a way to reduce it to 2x2 bimatrix? I know how to solve that but get stuck when it is 3x2 bimatrix which I don't see a dominating row.

Answer 1

The first strategy of the first player can be discarded because it is strictly dominated by the mixed strategy which assigns a probability of $\ \frac{1}{2}\ $ to each of the second and third pure strategies: \begin{align} \frac{1}{2}(4+0)&=2>1\ \ \text{and}\\ \frac{1}{2}(2+5)&=3.5>3\ . \end{align} So you can derive any Nash equilibrium of your $\ 3\times2\ $ bimatrix game from those of the game with the $\ 2\times2\ $ bimatrix $$ \begin{bmatrix} (4,2) & (2,3) \\ (0,3) & (5,2) \end{bmatrix}\ . $$