Hawk and Dove · evolutionarily stable strategies

Standingground

Two animals want the same thing. One escalates and keeps escalating; the other displays and backs off the moment things get serious. Two that back off will share. Two that escalate will fight, and the fight costs more than the thing was worth. That last line changes everything, and it is where property rules come from.

The rules

Why this is not a prisoner's dilemma

In a prisoner's dilemma, both defecting is the second-worst outcome. It is survivable, everyone can see it coming, and it is where the reasoning lands. Here, both escalating is the worst outcome on the board by a distance.

That inverts the logic of deterrence. The threat that keeps the peace is the one you would be mad to carry out, so the interesting question is not whether to escalate but whether anyone believes you will. Schelling built a career on that asymmetry, and the game is often called Chicken for the same reason.

Maynard Smith and Price (1973) introduced it to explain something biologists had long noticed: animals that could badly hurt each other mostly do not. Skyrms (1996) uses it for a different question, which is where the rule “leave it alone if it is already theirs” could possibly have come from.

Start from
Generation
0
not started
Escalating
—
of all encounters
Actually fighting
—
escalation meeting escalation
Average take
—
Who survives
The payoffs
Escalation against fighting drag or arrow keys to replay
Encounters where somebody escalates Encounters that become fights
The strategies
Across many populations
Things worth trying

Four runs that each show something

Press Fights are ruinous
Hawks and doves settle at exactly V over C, whatever share they started at. Nobody chose that number and no individual can improve on it.
Press Fights are cheap
Make the prize worth more than the injury and escalation simply dominates. The game stops being interesting, which is a useful thing to see.
Press Possession wins, and watch the two numbers
Escalation goes up, from a third of encounters to half, and fighting goes to almost nothing. Nobody became less aggressive. The aggression just stopped colliding.
Now press The mirror wins
Same settings, different starting population. Everyone yields when they own the thing and escalates when they do not. It works exactly as well, and looks nothing like property.
Turn off the visible asymmetry
The conditional strategies vanish from the roster, because there is nothing left for them to condition on, and the population falls back to the mixture. No asymmetry, no convention.
The argument

Why anyone cares

Turn on the asymmetry and something appears that nobody designed: a rule about who gets to keep things.

Hume's problem

Hume argued that property is a convention rather than a natural fact, and that it arises because everyone benefits from stable possession without anyone needing to agree to it. The obvious objection is that this still sounds like something people worked out. Where would such a rule come from among creatures that cannot work anything out?

What the model shows

The strategy above labelled Bourgeois escalates when it arrived first and yields when it did not. It is evolutionarily stable: a population of it cannot be invaded. Nothing about arriving first makes an animal likelier to win a fight. The asymmetry is arbitrary, and that is exactly why it works, because both sides can see it and it settles who does what.

The convention escalates more often than the population it replaced, and almost nobody gets hurt.

That is the result worth sitting with. Under the convention every owner escalates, so escalation is more common than in the mixed population, and fighting drops to nothing, because escalation never meets escalation. Nobody became less aggressive. The aggression stopped colliding.

The uncomfortable half

The mirror strategy is just as stable. Yield when you own the thing, take it when you do not. Populations reach it about as often, and once there it is as unshakeable as the other. It is not a worse rule by any measure the model has.

So the model gives Hume rather less than he wanted. It explains how an arbitrary asymmetry becomes a stable rule without anyone deciding anything. It does not explain why the rule we ended up with is the one that looks like property, and it offers no ground for saying that rule is the right one. Skyrms is explicit about this: the account is about how conventions form, not about which conventions deserve respect.

Where it sits next to the rest of the site

This is the third answer on this site to the question of how creatures that cannot reason end up coordinated. Wordless gets meaning out of reinforcement, Fair Shares gets an equal split out of dynamics, and this gets something like property out of an arbitrary difference. In each case the thing that emerges is real, stable, and not obviously the thing anyone would have chosen.

What this model is not

Contests here are between strangers with nothing at stake beyond one resource. Nobody remembers anyone, nobody is stronger than anyone else, there is no territory and no enforcement. Real ownership involves third parties who punish theft, which is a mechanism this game does not contain and which changes the answer substantially.

References

Sources

  1. Gintis, H. (2007). The evolution of private property. Journal of Economic Behavior & Organization, 64(1), 1–16.
  2. Hume, D. (2000). A treatise of human nature (D. F. Norton & M. J. Norton, Eds.). Oxford University Press. (Original work published 1739–1740)
  3. Maynard Smith, J. (1982). Evolution and the theory of games. Cambridge University Press.
  4. Maynard Smith, J., & Price, G. R. (1973). The logic of animal conflict. Nature, 246(5427), 15–18.
  5. Schelling, T. C. (1960). The strategy of conflict. Harvard University Press.
  6. Skyrms, B. (1996). Evolution of the social contract. Cambridge University Press.
  7. Sugden, R. (1986). The economics of rights, co-operation and welfare. Blackwell.