Solution to Hawk-Dove

Proof
From the payoff table:

Each player gains most by acting as a hawk while the other player acts as a dove.

Each player loses most when both act as hawks.

So each animal prefers to be a hawk if its opponent prefers to be a dove.

Thus there are two Nash equilibria:
 * $\left({\text{Hawk}, \text{Dove} }\right)$
 * $\left({\text{Dove}, \text{Hawk} }\right)$