In game theory, the Stag Hunt is a game first discussed by Jean-Jacques Rousseau. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Rousseau described a situation where two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. If an individual hunts stag, she must have the cooperation of her partner. An individual can get a hare by herself, but a hare is worth less than a stag. Game theory is a branch of applied mathematics that uses models to study interactions with formalised incentive structures (games). It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. ... Jean-Jacques Rousseau Jean Jacques Rousseau (June 28, 1712 – July 2, 1778) was a French philosopher, writer, political theorist, and self-taught composer of The Age of Enlightenment. ... Genera About 15 in 4 subfamilies. ... Genera Lepus Caprolagus Pronolagus Hares and Jackrabbits belong to family Leporidae, and mostly in genus Lepus. ...

An example of the payoff matrix for the Stag Hunt is as follows: A payoff matrix or payoff function is a concept in game theory which shows what payoff each player will receive at the outcome of the game. ...

A Stag Hunt has also been considered by David Hume in his discussions of the social contract. David Hume David Hume (April 26, 1711 – August 25, 1776) was a Scottish philosopher and historian and, with Adam Smith and Thomas Reid among others, one of the most important figures in the Scottish Enlightenment. ... Social contract is a phrase used in philosophy, political science, and sociology to denote a real or hypothetical agreement within a state regarding the rights and responsibilities of the state and its citizens, or more generally a similar concord between a group and its members. ...

Formal definition

Formally, a Stag Hunt is a game with two Nash equilibria one that is risk dominant another that is payoff dominant. The following matrix illustrates a Stag hunt, where a>b>=d>c.

The Stag Hunt and social cooperation

Although most authors focus on the Prisoner's Dilemma as the game that best represents the problem of social cooperation, some authors believe that the Stag Hunt represents an equally (or more) interesting context in which to study cooperation and its problems (for an overview see Skyrms 2004). Will the two prisoners cooperate to minimise total loss of liberty or will one of them, trusting the other to cooperate, betray him so as to go free? The prisoners dilemma is a type of non-zero-sum game. ... Co-operation refers to the practice of people or greater entities working in common with commonly agreed-upon goals and possibly methods, instead of working separately in competition. ... Co-operation refers to the practice of people or greater entities working in common with commonly agreed-upon goals and possibly methods, instead of working separately in competition. ...

References

Skyrms, Brian. (2004) The Stag Hunt and Evolution of Social Structure Cambridge: Cambridge University Press.