What is the stag hunt in simple terms?

If two people team up they can catch a big stag, but if you worry your partner will run off after a hare, you may settle for a hare you can surely catch alone.

How does it differ from the prisoner's dilemma?

In the prisoner's dilemma, defecting pays more even if the other cooperates; in the stag hunt, cooperating is best if you trust the other to cooperate. The core problem is trust, not the temptation to defect.

Stag Hunt

📈 Economics By CampusDown Wiki Editorial Team Last updated October 27, 2026 Views 7

The stag hunt is a game-theory model named after the hunting parable in Jean-Jacques Rousseau's 1755 Discourse on Inequality. If both hunters pursue a stag they win a large reward, but if one goes after a hare the stag hunter gets nothing, while a hare can be caught reliably alone. It is a classic coordination game capturing the choice between cooperation and safety, in other words the problem of trust.

Contents

1. The parable and the game
2. Equilibrium selection and evolutionary game theory
3. Experiments and applications
4. FAQ
5. References

The parable and the game

Rousseau (1755) wrote that hunters cooperating to catch a stag would keep their posts, but if a hare happened to pass within reach of one of them, he would chase it without scruple and spoil his companions' hunt. Hume (1739–1740) gave similar examples of cooperation, such as rowing a boat and draining a meadow. As a game, if both choose stag each gets 4, if both choose hare each gets 2, and if only one chooses stag the stag hunter gets 0 while the hare hunter gets 2 (or 3). The game has two Nash equilibria, both stag and both hare. Unlike the prisoner's dilemma, cooperating is best if you are assured the other will cooperate, so it is also called the assurance game. The problem is not the temptation to defect but strategic uncertainty about whether the other can be trusted.

Equilibrium selection and evolutionary game theory

Schelling (1960) stressed the role of focal points that align expectations in such coordination problems. Harsanyi and Selten (1988) distinguished the payoff-dominant equilibrium, which gives everyone more (both stag), from the risk-dominant equilibrium, which is less risky when the other's action is uncertain (both hare). Kandori, Mailath and Rob (1993) and Young (1993) showed that in evolutionary dynamics with random mistakes the risk-dominant equilibrium is selected in the long run, and Carlsson and van Damme (1993) reached a similar conclusion in global games with slightly incomplete information. Skyrms (2004) treated the stag hunt as the central model of the social contract and analyzed how network structure and signaling help cooperation evolve.

Experiments and applications

In experiments by Van Huyck, Battalio and Beil (1990) and Cooper et al. (1990), participants frequently converged on the safe equilibrium rather than the more rewarding cooperative one, a pattern known as coordination failure. Battalio, Samuelson and Van Huyck (2001) reported that the size of payoff differences affects these learning outcomes. In international relations, Jervis (1978) analyzed cooperation between states under the security dilemma as a stag hunt, and Diamond and Dybvig's (1983) bank run model shares the same structure, with an equilibrium in which everyone keeps their deposits coexisting with one in which everyone withdraws. Technology standard adoption and climate cooperation are also often discussed in this framework.

FAQ

What is the stag hunt in simple terms?: If two people team up they can catch a big stag, but if you worry your partner will run off after a hare, you may settle for a hare you can surely catch alone.
How does it differ from the prisoner's dilemma?: In the prisoner's dilemma, defecting pays more even if the other cooperates; in the stag hunt, cooperating is best if you trust the other to cooperate. The core problem is trust, not the temptation to defect.

Sources reviewed: 2026-10-26

References

Rousseau, J.-J. (1755). Discours sur l'origine et les fondements de l'inégalité parmi les hommes. Amsterdam: Marc-Michel Rey.
Hume, D. (1739–1740). A Treatise of Human Nature. London: John Noon.
Skyrms, B. (2004). The Stag Hunt and the Evolution of Social Structure. Cambridge: Cambridge University Press.
Harsanyi, J. C., & Selten, R. (1988). A General Theory of Equilibrium Selection in Games. Cambridge, MA: MIT Press.
Schelling, T. C. (1960). The Strategy of Conflict. Cambridge, MA: Harvard University Press.
Jervis, R. (1978). Cooperation under the security dilemma. World Politics, 30(2), 167–214.
Kandori, M., Mailath, G. J., & Rob, R. (1993). Learning, mutation, and long run equilibria in games. Econometrica, 61(1), 29–56.
Young, H. P. (1993). The evolution of conventions. Econometrica, 61(1), 57–84.
Van Huyck, J. B., Battalio, R. C., & Beil, R. O. (1990). Tacit coordination games, strategic uncertainty, and coordination failure. American Economic Review, 80(1), 234–248.
Cooper, R., DeJong, D. V., Forsythe, R., & Ross, T. W. (1990). Selection criteria in coordination games: Some experimental results. American Economic Review, 80(1), 218–233.
Carlsson, H., & van Damme, E. (1993). Global games and equilibrium selection. Econometrica, 61(5), 989–1018.
Battalio, R., Samuelson, L., & Van Huyck, J. (2001). Optimization incentives and coordination failure in laboratory stag hunt games. Econometrica, 69(3), 749–764.
Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401–419.

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This article was last updated on October 27, 2026. It is based on widely recognized original works and textbooks; when citing it in a paper, please check the original sources listed in the references.