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← Theoretical 2

Q92 — Hawk-Dove-Retaliator Game Theory and Evolutionarily Stable Strategies

Theoretical 2 Real exam question — full text reproduced under IBO's CC BY-NC-SA 4.0 license
Aggression, Territoriality & Social Structure

In their seminal paper from 1973, J.M. Smith and G.R. Price used computer modeling to investigate intraspecific animal interactions. They assumed two mechanisms by which animals can inflict damage: soft, also known as “conventional” (e.g. snakes wrestling) and hard, also known as “dangerous” (e.g. snakes biting each other). They assigned positive rewards for the early retreat (accounting for saved resources) or winning (accounting for obtained resources) and negative rewards for receiving damage. Simulations were performed for various matches of stereotyped behaviors (“Mouse”, “Hawk”, “Bully”, “Retaliator”, and “Prober-Retaliator”). Averages of final rewards for each match are summarized below, with more positive values indicative of a more favorable outcome for the individual with that behavior type. For example, a “Bully” gets 80.0 points in a match against a “Mouse”, while the “Mouse” gets 19.5 points in a match against the “Bully”.

Focal strategy ↓ vs. opponent → “Mouse” “Hawk” “Bully” “Retaliator” “Prober-Retaliator”
“Mouse” 29.0 19.5 19.5 29.0 17.2
“Hawk” 80 -19.5 74.6 -18.1 -18.9
“Bully” 80 4.9 41.5 11.9 11.2
“Retaliator” 29.0 -22.3 57.1 29.0 23.1
“Prober-Retaliator” 56.7 -20.1 59.4 26.9 21.9

Table: average payoff to the row (focal) strategy in a match against the column (opponent) strategy.

Assuming that in a mixed population, all fights occur between randomly chosen pairs, determine whether the following statements are true or false.

A. In a population with 90% "hawks" and 10% of "mice", "mice" would eventually go extinct.
B. A population composed of "retaliators" and "mice" would most likely have a stable composition from generation to generation.
C. If a population is comprised of 99.9% "mice", then "mouse" is surely an evolutionarily stable strategy
D. If a population comprises 99.9% "retaliators", then "retaliator" is surely an evolutionarily stable strategy.
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Question reproduced from IBO 2022, Theoretical Paper 2, licensed under CC BY-NC-SA 4.0 — attributed to the International Biology Olympiad. Open the full exam PDF · Community solutions (unofficial)