Stag hunt
From Biocrawler, the free encyclopedia.
In game theory, the Stag Hunt is a game which describes a conflict between safety and social cooperation. Other names for it or its variants include "assurance game", "coordination game", and "trust dilemma". Jean-Jacques Rousseau described a situation where two individuals go out on a hunt. Each can individually choose to hunt a stag or hunt a hare. Each player must choose an action without knowing the choice of the other. If an individual hunts stag, she must have the cooperation of her partner in order to suceed. An individual can get a hare by herself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.
An example of the payoff matrix for the Stag Hunt is as follows:
| Stag | Hare | |
|---|---|---|
| Stag | 4, 4 | 0, 3 |
| Hare | 3, 0 | 3, 3 |
| Contents |
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.
| Stag | Hare | |
|---|---|---|
| Stag | a, a | c, b |
| Hare | b, c | d, d |
Often, games with a similar structure but without a risk dominant Nash equilibrium are called Stag Hunts. For instance if a=2, b=1, c=0, and d=1. While (Hare, Hare) remains a Nash equilibrium, it is no longer risk dominant. Nonetheless many would call this game a Stag Hunt.
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).
There is a substantial relationship between the Stag Hunt and the Prisoner's Dilemma. In biology many circumstances that have been described as Prisoner's Dilemma might also be interpreted as a Stag Hunt, depending on how fitness is calculated. It is also the case that some human interactions that seem like Prisoner's Dilemmas may in fact be Stag Hunts. For example, suppose we have a Prisoner's Dilemma with the following payoffs:
| Cooperate | Defect | |
|---|---|---|
| Cooperate | 4, 4 | 0, 5 |
| Defect | 5, 0 | 3, 3 |
But occasionally players who defect against cooperators are punished for their defection. For instance, suppose that the expected punishment is -2, then the imposition of this punishment turns the above Prisoner's Dilemma into the Stag Hunt given at the introduction.
Examples of the Stag Hunt
In addition to the example suggested by Rouseau, David Hume provides a series of examples that are Stag Hunts. One example addresses two individuals who must row a boat. If both choose to row they can successfully move the boat. However, if one doesn't the other wastes his effort. Hume's second example involves two neighbors wishing to drain a meadow. If they both work to drain it they will be successful, but if either fails to do his part the meadow will not be drained.
There are several animal behaviors that have been described as Stag Hunts. For example, the coordination of slime molds. In times of stress, individual bacteria will aggregate to form one large body. Here if they all act together they can successfully reproduce, however the success depends on the cooperation of many bacteria. Also, the hunting practices of orca (known as carousel feeding) are an example of a Stag Hunt. Here orcas cooperatively corral large schools of fish to the surface and stun them by hitting them with their tails. Since this requires that fish not have any mechanism for escape, it requires the cooperation of many orcas.
References
Skyrms, Brian. (2004) The Stag Hunt and Evolution of Social Structure Cambridge: Cambridge University Press.
External links
- The Stag Hunt at GameTheory.net (http://www.gametheory.net/Dictionary/Games/StagHunt.html)
- The Stag Hunt (pdf) (http://www.lps.uci.edu/home/fac-staff/faculty/skyrms/StagHunt.pdf) by Brian Skyrms
| Topics in game theory |
|---|
| Evolutionarily stable strategy - Mechanism design - No-win - Winner's curse - Zero-sum |
| Games: Prisoner's dilemma - Chicken - Stag hunt - Ultimatum game - Matching pennies ... |
| Related topics: Mathematics - Economics - Behavioral economics - Evolutionary biology - Evolutionary game theory - Population genetics - Behavioral ecology |
| [ edit ] |
