Category: economics
Type: model
Associated thinker(s): Jean-Jacques Rousseau
Original publication or approximate period: Rousseau, Discourse on the Origin and Foundations of Inequality (1755); later formalized in game theory
Difficulty: Intermediate
Themes: coordination, trust, risk
Related experiments: The Prisoner’s Dilemma; The Tragedy of the Commons; The State of Nature
Two hunters can each choose to hunt a stag or a hare. A stag can only be caught if both hunters cooperate, and it feeds both well. A hare can be caught by one hunter alone, but it is a smaller meal. If one hunter goes after the stag and the other goes after a hare, the stag hunter gets nothing.
An illustrative payoff table is below. Each cell lists the payoffs to Player 1 and Player 2.
| Player 2 hunts stag | Player 2 hunts hare | |
|---|---|---|
| Player 1 hunts stag | 4, 4 | 0, 3 |
| Player 1 hunts hare | 3, 0 | 3, 3 |
When cooperation is best for everyone but risky, what lets people trust each other enough to coordinate?
Unlike the Prisoner’s Dilemma, the stag hunt has no dominant strategy: hunting stag is a best response if the other hunter chooses stag, while hunting hare is a best response if the other chooses hare. With the illustrative payoffs above, both hunters choosing stag and both choosing hare are Nash equilibria. The stag equilibrium gives both a higher payoff (4, 4 rather than 3, 3), so it is payoff-dominant. The hare equilibrium is risk-dominant for this payoff table: under an equal-likelihood estimate of the other hunter’s choice, hare yields 3 while stag has an expected payoff of 2. This risk-dominance result depends on the payoffs and the stated belief criterion; it is not true of every game called a stag hunt.
In the Prisoner’s Dilemma, defection is individually dominant even when the other player cooperates, and mutual cooperation is not a Nash equilibrium. In the stag hunt, the best response depends on the other player’s choice, and mutual cooperation is an equilibrium, but a player risks getting nothing by hunting stag alone.
Joining a protest, adopting a shared standard, or investing in a joint project can serve as teaching analogies for coordination problems. They are not predictions made by this two-player model. In a real case, institutions, communication, or reputation might affect expectations, payoffs, or the salience of a coordinated choice; whether they help depends on the details.
Payoff-dominance favours the stag equilibrium because both hunters do better there. Risk-dominance favours the hare equilibrium with the payoffs shown above; changing payoff relations can change which equilibrium is risk-dominant. Evolutionary analyses add assumptions about population structure and how strategies change over time, so the basic matrix alone does not determine which outcome a population settles into. Brian Skyrms uses the stag hunt as a model for questions about social contracts; that is a broader interpretation, not a conclusion entailed by the two-player payoff table.
The numbers in the table are illustrative, not part of Rousseau’s original story. In Part II of the Discourse on Inequality, Rousseau describes hunters who understand the need to keep their positions when pursuing a deer, but who may leave the hunt to chase a passing hare. That passage is a verbal scenario, not a formal payoff matrix or equilibrium analysis. The formal model depends on the ordering of payoffs. The stag hunt is not a Prisoner’s Dilemma: in the stag hunt the obstacle is coordination under risk, rather than a dominant incentive to defect.
Many-player versions can require cooperation from a threshold number of participants, or even full cooperation. Their equilibrium and coordination problems can differ from those in the two-person model.
Rousseau’s Part II hunting passage was consulted in Ian Johnston’s English translation. The Stanford Encyclopedia of Philosophy entry on the Prisoner’s Dilemma was consulted in §8 and compares the stag hunt with the Prisoner’s Dilemma; its payoff matrix is the source for the illustrative numbers and the risk-dominance condition. Brian Skyrms’s “The Stag Hunt” was consulted for the model’s assumptions, equilibrium interpretation, and evolutionary extensions. The 1755 publication date was checked against Encyclopaedia Britannica’s entry on the work. Rousseau’s passage supplies the story, not the formal game; payoff numbers and the two-player matrix are later modeling choices. Modern applications in this article are teaching analogies, not established historical examples or empirical claims.
Research check: 2026-11-01. Relevant passages, source access levels, and limitations are recorded in research/source-review-batch17-item-stag-hunt.json. This is an original educational explanation, not a substitute for the primary text or technical game-theory analyses.