Stag hunt

Stag hunt

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 in which 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 a stag, he must have the cooperation of his partner in order to succeed. An individual can get a hare by himself, but a hare is worth less than a stag. This is taken to be an important analogy for social cooperation.

The stag hunt differs from the Prisoner's Dilemma in that there are two Nash equilibria: when both players cooperate and both players defect. In the Prisoners Dilemma, however, despite the fact that both players cooperating is Pareto efficient, the only Nash equilibrium is when both players choose to defect.

An example of the payoff matrix for the stag hunt is pictured in Figure 2.

Formal definition

Formally, a stag hunt is a game with two pure strategy Nash equilibria - one that is risk dominant another that is payoff dominant. The payoff matrix in Figure 1 illustrates a stag hunt, where a>bge d>c. 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.In addition to the pure strategy Nash equilibria there is one mixed strategy Nash equilibrium. This equilibrium depends on the payoffs, but the risk dominance condition places a bound on the mixed strategy Nash equilibrium. No payoffs (that satisfy the above conditions including risk dominance) can generate a mixed strategy equilibrium where Stag is played with a probability higher than one half. The best response correspondences are pictured here.-

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 as pictured in Figure 3.

But occasionally players who defect against cooperators are punished for their defection. For instance, if 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.Payoff matrix | Name = Fig. 3: Prisoner's dilemma example
2L = Cooperate | 2R = Defect
1U = Cooperate | UL = 4, 4 | UR = 0, 5
1D = Defect | DL = 5, 0 | DR = 3, 3

Examples of the stag hunt

In addition to the example suggested by Rousseau, 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 unicellular protists 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 individual protozoa. 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

* [http://www.gametheory.net/Dictionary/Games/StagHunt.html The stag hunt at GameTheory.net]
* [http://www.lps.uci.edu/home/fac-staff/faculty/skyrms/StagHunt.pdf The stag hunt (pdf)] by Brian Skyrms


Wikimedia Foundation. 2010.

Игры ⚽ Нужен реферат?

Look at other dictionaries:

  • stag hunt — noun • • • Main Entry: ↑stag …   Useful english dictionary

  • stag hunt —    A form of social disapproval custom noted only in Devon, but akin to the more widespread *rough music ceremony. In the known instances, the hunt was prompted by some form of sexual misconduct or deviancy in the community, usually adultery or… …   A Dictionary of English folklore

  • Stag Hunt Mosaic — The emblema of the Stag Hunt mosaic. The Stag Hunt mosaic (c. 300 BCE) by Gnosis is a mosaic from a wealthy home, the so called House of the Abduction of Helen (or House of the Rape of Helen ), in Pella, the capital of the Macedonian Kingdom.… …   Wikipedia

  • hunt — hunt1 [hʌnt] v [: Old English; Origin: huntian] 1.) [I and T] to chase animals and birds in order to kill or catch them ▪ the slopes where I hunted deer as a kid ▪ Wolves tend to hunt in packs (=hunt in groups) . 2.) to look for someone or… …   Dictionary of contemporary English

  • White Stag Leadership Development Program — White Stag Leadership Development is a non profit organization founded on the Monterey Peninsula, California, in 1958 by Dr. Béla H. Bánáthy. The youth run program prepares and produces two week long summer camps for other youth age 11 17 each… …   Wikipedia

  • Berkeley Hunt — The Berkeley Hunt is a hunt in England. Its country lies in Gloucestershire and South Gloucestershire, between Gloucester and Bristol. The hill country above Dursley and Wotton under Edge is hunted mainly in March and early April, and adjoins the …   Wikipedia

  • William Hunt (officer of arms) — William George Hunt, TD, FCA is the current Windsor Herald of Arms in Ordinary at the College of Arms in London. Hunt worked for many years in the City of London as a chartered accountant. He was appointed as Portcullis Pursuivant of Arms in… …   Wikipedia

  • Best response — In game theory, the best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players strategies as given (Fudenberg Tirole 1991, p. 29; Gibbons 1992, pp. 33–49). The concept of a …   Wikipedia

  • Deer — This article is about the ruminant animal. For other uses, see Deer (disambiguation). Fawn and Stag redirect here. For other uses, see Fawn (disambiguation) and Stag (disambiguation). Deer Temporal range: Early Oligocene–Recent …   Wikipedia

  • Coordination game — In game theory, coordination games are a class of games with multiple pure strategy Nash equilibria in which players choose the same or corresponding strategies. Coordination games are a formalization of the idea of a coordination problem, which… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”