Definition:Hawk-Dove

Definition

Hawk-Dove is an instance of a class of games whose mechanics are as follows:

There are two players: animals fighting over some prey.

Each can either behave like:

a dove, in which they cooperate and share

or:

a hawk, in which they fight for full control.

If they both act as doves, they both obtain a goodly part of the prey.

If they both act as hawks, they lose control of the prey, and the latter escapes, so they receive nothing.

If one acts as a hawk and the other as a dove, the hawk controls the entire prey, granting the dove some small portion.

The payoff table of Hawk-Dove is as follows:

		$\text B$
$\text A$		$\begin{array} {r {{\|}} c {{\|}} } & \text{Dove} & \text{Hawk} \\ \hline \text{Dove} & 3, 3 & 1, 4 \\ \hline \text{Hawk} & 4, 1 & 0, 0 \\ \hline \end{array}$

		$\text B$
$\text A$		$\begin{array} {r {{\|}} c {{\|}} } & \text{Dove} & \text{Hawk} \\ \hline \text{Dove} & 3, 3 & 1, 4 \\ \hline \text{Hawk} & 4, 1 & 0, 0 \\ \hline \end{array}$

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:

$\tuple {\text{Hawk}, \text{Dove} }$

$\tuple {\text{Dove}, \text{Hawk} }$