Hawk-Dove Game

A symmetric 2x2 conflict game used to model animal contests.

Ask the Game theory assistant 1 min read · Updated September 9, 2026

Definition

Payoffs: $u(H,H)=(v-c)/2$ , $u(H,D)=v$ , $u(D,H)=0$ , $u(D,D)=v/2$ for resource value $v$ and fight cost $c$ .

When $c>v$ , the ESS is mixed with $x_H^*=v/c$ .

Hawks always escalate; Doves always retreat. Neither pure strategy is evolutionarily stable when escalation is costly.

Populations settle at a mix where the expected payoff to Hawks and Doves equalizes.

With $v=2,c=4$ : $x_H^*=1/2$ , giving expected payoff $1/2$ for both types.

Observed frequencies of aggressive vs. submissive individuals in many species approximate mixed ESS.

Equivalent to Chicken in economics when costs exceed rewards.

Under replicator dynamics, trajectories converge to the mixed ESS from any interior start.

Animal-conflict theory, business "chicken" dynamics, and territorial disputes.

Foundational example in evolutionary stability analysis.

Assembled from the ReLU.chat curated knowledge base. These explanations are concise on purpose; check the sources for anything important.