Hawk and Dove Game

Evolutionary Game Theory: Hawk-Dove Model

Structure

• Similar to the game “Chicken” with 2 pure strategy Nash equilibria:
  • (Dove, Hawk)
  • (Hawk, Dove)

Interpretation

• Key Questions:
  • What bird mutation (hawk or dove) is successful given a certain population?
  • Do stable Hawk/Dove bird populations exist such that mutations are not successful?
    • This relates to evolutionary stability.

Mixed Equilibrium = Evolutionary Stable Equilibrium

• Equation:

  $$p\cdot \frac{V}{2}+(1-p)\cdot 0=p\cdot V+(1-p)\cdot \frac{(V-C)}{2}$$

• Therefore, solving gives:

  $$p=1-\frac{V}{C}$$

• Interpretation:

  • The evolutionary stable proportion of Hawks and Doves is $\frac{V}{C}$.
  • Higher values of resource $V$ and lower fighting costs $C$ lead to a higher proportion of Hawks.
  • If $V>C$, all will be Hawks.