Here is a description of the Hawk and Dove:

HAWK: very aggressive, always fights for some resource.

DOVE: never fights for a resource -- it displays in any conflict and if it is attacked it immediately withdraws before it gets injured.


Equation #1:

 Eq. 1. Payoff(to Strat., when vs. a Strat.) =

[(chance of win) * (resource value - cost of win)]
+
[(chance of loss) * cost of loss]


 Action

Benefit or Cost (arbitrary units)

 Gain Resource + 50
Lose Resource 0
Injury to Self - 100
 Cost of Display to Self - 10


Payoff to Hawk when vs. Hawk:
 Eq. 2: E(H,H) = (0.5 * 50) + (0.5 * -100) = 25 - 50 = -25

 


Payoff to Hawk when vs. Dove:

 Eq. 3: E(H,D) = 1.0 * 50 - 0 = +50

 


Payoff to Dove when vs. Hawk:

 Eq. 4: E(D,H) = 0 * 50 + 1.0 * 0 = 0


 

Payoff to Dove when vs. Dove:
 Eq. 5: E(D,D) = (0.5) * (50 - 10) - (0.5) * (-10) = +15


Here is the payoff matrix for this particular version of the Hawk vs. Dove game:

 

 Opponent

 

Focal Strategy

 Hawk

 Dove

 Hawk

-25 +50

 Dove

0 +15


the fitness of Hawk, W(H), is:

 Eq. 8: W(H) = h * E(H,H) + (1-h) * E(H,D)

 

 

 

 

 

 

 


the fitness of Dove, W(D) is:

 Eq. 9: W(D) = h * E(D,H) + (1-h) * E(D,D)