Trustfalls
Two hunters can bring down a stag together and eat well. Either can catch a hare alone: small, certain, and no help required. Nobody here is tempted to cheat and nobody gains by defecting. Everyone hunting stag is stable, better for all of them, and needs no enforcement whatsoever. Populations still end up on the hare.
Why this is not a temptation problem
In a prisoner's dilemma the difficulty is that betrayal pays. Here it does not. If your partner hunts stag, your best move is to hunt stag too. Both of you doing so is an equilibrium nobody wants to leave.
| You / them | They hunt stag | They take the hare |
|---|---|---|
| You hunt stag | 4.8 each. The best available to anyone. | 0 for you. You cannot take a stag alone. |
| You take the hare | 3 for you, 0 for them. | 3 each. Nobody is hurt and nobody is fed well. |
Hare pays the same whatever anyone else does. That is the entire asymmetry. Stag is worth more and costs you everything if you are the only one who shows up, so the question is never what people want. It is what they expect of each other.
Rousseau put it in the Second Discourse in 1755. Skyrms argues it models the social contract better than the prisoner's dilemma does, precisely because there is nothing here to enforce.
Where the boundaries actually fall
Every combination of stag payoff and starting share, coloured by how much of the grid ends up hunting stag. If the outcome depended on how many started, the boundaries would run diagonally. They do not.
Five runs that each show something
Why anyone cares
Almost every popular account of why cooperation is hard is a story about temptation. This game has none, and cooperation is still hard, which means the temptation story was never the whole problem.
Rousseau's hunters
The image is from the Second Discourse (1755). A group agrees to take a stag, which requires all of them to hold their positions. A hare passes within one man's reach, and he takes it, because a hare in hand feeds him tonight and the stag depends on everyone else keeping faith. Rousseau's point is not that the man is wicked. He is being reasonable. What he lacks is any assurance about the others.
What makes it different from the prisoner's dilemma
In a prisoner's dilemma, defection dominates: whatever the other does, you do better betraying them. The cooperative outcome is not an equilibrium at all, and holding it together needs punishment, reputation, repetition, or something else brought in from outside.
Here mutual stag is an equilibrium already. Nobody has to be watched, punished or bound by contract. Both of you hunting stag is stable on its own terms, and better for both of you than the alternative. So the question is not how to stop people defecting. It is how a population that would all prefer the better arrangement manages to sit in the worse one indefinitely.
Nobody defected. Nobody was tempted. The better outcome was available the entire time.
Skyrms's case for it
Skyrms (2004) argues the stag hunt is the better model of the social contract, and that political philosophy has spent too long on the prisoner's dilemma. If the fundamental problem were temptation, the fundamental solution would be enforcement, and the state earns its keep by being the enforcer. If the fundamental problem is assurance, then what a society needs is not a bigger stick but reliable expectations, and the institutions that matter are the ones that make people legible to each other.
The part the grid adds
Work out the algebra and there is a threshold: hunt stag if you are confident enough that your partner will. With the payoffs above that comes to a specific share of your partners. It is a real number and it moves smoothly as the payoffs change.
Put the same hunters on a lattice, where they play the people next to them rather than the population at large, and that number stops mattering. What binds instead is how many of your neighbours must hunt stag before you match what a hare hunter collects from everyone. Neighbours come in whole numbers. So the threshold is an integer, and it moves in steps.
That is why the phase diagram above has vertical boundaries sitting exactly on the whole-number lines. Take the stag payoff from 4.5 to 5.0 and the requirement drops from six neighbours to five, and a population that was certain to fail becomes a population that is certain to succeed. It is also why the same payoffs can succeed with eight neighbours and fail with four: the arithmetic rounds differently. Nothing about anyone's preferences changed.
What this model is not
Agents here imitate whoever near them is doing better. They do not reason, form beliefs about each other, make promises, or choose whom to interact with. The assurance problem Rousseau describes is fundamentally about expectation, and expectation is the one thing this model has no representation of. Read it as a demonstration that structure alone can decide which equilibrium a population reaches, not as an account of how hunters actually think.
Sources
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- Rousseau, J.-J. (1997). Discourse on the origin and foundations of inequality among men (V. Gourevitch, Trans.). Cambridge University Press. (Original work published 1755)
- Skyrms, B. (1996). Evolution of the social contract. Cambridge University Press.
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