Hawk-Dove Game: Evolutionary Game Theory & the ESS

Contest Payoffs

Resource value V 4.0

Injury cost C 8.0

Mutation rate 1%

Simulation speed 1.0x

Population

Hawk 50%Dove 50%

Gen. mean fitness

0.00

ESS target p*

50.0%

Generation

|p − p*|

0.000

How it works

The Hawk-Dove game models animals contesting a resource worth V. A Hawk always escalates to a fight; a Dove displays but retreats if the opponent escalates. When two Hawks meet, one is injured at cost C. The symmetric payoff matrix:

           vs Hawk        vs Dove
Hawk:    (V − C) / 2         V
Dove:        0             V / 2

With population fraction p playing Hawk, expected payoffs are:

W(Hawk) = p·(V−C)/2 + (1−p)·V
W(Dove) = (1−p)·V/2

Each generation, p evolves under the replicator equation dp/dt = p(1−p)[W(Hawk) − W(Dove)], the standard model of natural selection acting on strategy frequency. When the injury cost exceeds the resource value (C > V), pure Hawk is unstable and the population settles at the mixed evolutionarily stable strategy:

p* = V / C   (clamped to [0, 1])

At p* neither strategy can invade — a rare mutant Hawk in an all-Dove population does better being a Hawk, and a rare mutant Dove in a mostly-Hawk population does better being a Dove, so the mix is self-correcting. If C ≤ V, fighting is never more costly than losing the resource, so the population is driven fully Hawk (p* = 1). A small mutation rate keeps both strategies present and lets you see the pull back toward p* after a perturbation.

Hawk (escalates) Dove (displays / retreats)

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