Solution to Hawk-Dove
Jump to navigation
Jump to search
Solution to Hawk-Dove
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.
Proof
From the payoff table:
$\text B$ | ||
$\text A$ | $\begin{array} {r {{|}} c {{|}} } & \text{Dove} & \text{Hawk} \\ \hline \text{Dove} & 3, 3 & 1, 4 \\ \hline \text{Hawk} & 4, 1 & 0, 0 \\ \hline \end{array}$ |
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:
- $\tuple {\text{Hawk}, \text{Dove} }$
- $\tuple {\text{Dove}, \text{Hawk} }$
Sources
- 1994: Martin J. Osborne and Ariel Rubinstein: A Course in Game Theory ... (previous) ... (next): $2.3$: Examples: Example $16.3$