Two animals find the same patch of food. Each can fight for it like a hawk or back off like a dove.
Two doves share it. A hawk meeting a dove takes all of it, and the dove leaves with nothing. Two hawks fight, and the injuries cost more than the food is worth.
The food is worth 4. Two doves get 2 each. Hawk against dove: 4 for the hawk, 0 for the dove. Two hawks: minus 1 each.
You are Animal A
Watch one round, or choose now.
Animal A
or
You
Animal A
?
You
Animal B
or
The other animal
Animal B
?
The other animal
The other animal picks at random here, like a coin toss.
The whole game on one grid
Every pair of choices and what each side gets: yours first, then theirs. Each number is a payoff.
Step 0 of 3
The cards are face down. Turn them, then step through which squares are stable.
What do you think they'll do?
Your best move depends on what you expect from the other animal. Drag to set how likely you think it is they pick Hawk.
What it teaches
Aggression pays only while it is rare, so a population settles at a mix rather than on a type.
The usual mistakeAsking which type wins, and expecting the population to end up entirely hawk because aggression beats passivity in a head to head comparison.
The checkAsk what a hawk earns in a population that is already mostly hawk. The frequency at which that equals the dove payoff is the answer.
What people actually do
Frequency-dependent strategies cycle instead of settling
The theory says
In a population game with no evolutionarily stable pure strategy, the static analysis gives a mixed equilibrium, and a population at the equilibrium frequencies is at rest, with selection removing any deviation.
People actually
Male side-blotched lizards occur in three morphs standing in a strict rock-paper-scissors relation, and their frequencies in the wild oscillate over a cycle of several years rather than holding at the predicted mixture. The analogous laboratory and simulation result is that populations of adaptive agents orbit the equilibrium without converging to it.
Why is still argued over.
In the real world
Real world
Litigate or cross-license in the smartphone patent wars
From about 2010 the smartphone industry fought a long run of patent suits across many jurisdictions, Apple against Samsung being the most visible, with Nokia, Motorola, HTC and Microsoft involved in others. A firm that litigated hard while most of the industry cross-licensed could extract terms, but once several large firms were fighting at once the legal costs and the injunction risk fell on everybody, and most of the disputes ended in settlements and licences, including the global settlement between Apple and Samsung in 2018.
Aggression pays only while it is rare, so the industry does not settle on a type but on a proportion, with some firms litigating and most licensing at any one time. That population reading is what distinguishes hawk-dove from chicken, which is the same payoff structure read as a single standoff between two named players. The inference is that the aggressive suits were mostly optimising for the terms of an eventual licence rather than for an injunction that would stop a rival selling, which is why the stable state is a mixture rather than an industry of litigators.
Fiction: Squid Game
The night the lights go out in the dormitory
The players are held between rounds in a shared dormitory, and because the prize grows with every death, killing a rival improves the position of everyone left. While only a few are willing to attack, those few do well. On the night the lights go out and many turn on each other at once, the violence costs attackers as heavily as bystanders, and afterwards the players organise into teams and the share willing to attack falls back.
What is being described is the proportion of a population behaving aggressively rather than a single standoff between two named people, and that proportion is self-limiting because aggression only pays while it is uncommon, which is the hawk-dove reading of the same payoffs that chicken gives to two individuals. The inference is that most players were optimising for survival to the next round rather than for the size of the pot, which is why the aggressive share collapses as soon as it becomes dangerous to hold.
Cyclic population gameBest responses run in a cycle rather than meeting head on, so the population spirals into the mix rather than approaching it along a line. Not on the wall yet.