Mixed ESS

Resource < cost; V = 1; C = 2

Opponent: Hawk Dove

Actor: Hawk

Dove

-1/2 1

0 1/2

-1/2 < 0, so Doves can invade Hawks

1 > 1/2, so Hawks can invade doves

ESS = mix of Hawks and Doves => mixed ESS

If frequency of Hawks is p, and Doves is 1-p and at the ESS

the fitness of Hawks = the fitness of Doves, then

WH = 1/2(V-C)p + V(1-p)

WD = 1/2(1-p) which after substituting payoffs is

(-1/2)p + (1-p) = (0)p + (1/2)(1-p); 1 - 3p/2= 1/2 - p/2; 1/2 = p