Write the formula for equivalent resistance of resistors in parallel.

For $n$ resistors connected in parallel, the equivalent resistance $R_{eq}$ is given by:

$$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$

We have three resistors, each with a resistance of $2 \, \Omega$. So, $R_1 = R_2 = R_3 = 2 \, \Omega$.

$$\frac{1}{R_{eq}} = \frac{1}{2 \, \Omega} + \frac{1}{2 \, \Omega} + \frac{1}{2 \, \Omega}$$

$$R_{eq} = \frac{2 \, \Omega}{3}$$ $$R_{eq} \approx 0.6666... \, \Omega$$

Rounding to two decimal places, $R_{eq} \approx 0.67 \, \Omega$.

The calculated value matches option A.

The final answer is $\text{A. } 0.67 \, \Omega$.