Chicken (game)

The name "hawk–dove" refers to a situation in which there is a competition for a shared resource and the contestants can choose either conciliation or conflict; this terminology is most commonly used in biology and evolutionary game theory.

[1] The game has also been used to describe the mutual assured destruction of nuclear warfare, especially the sort of brinkmanship involved in the Cuban Missile Crisis.

If neither player swerves, the result is a costly deadlock in the middle of the bridge or a potentially fatal head-on collision.

The phrase game of chicken is also used as a metaphor for a situation where two parties engage in a showdown where they have nothing to gain and only pride stops them from backing down.

It is played by choosing a long, straight road with a white line down the middle and starting two very fast cars toward each other from opposite ends.

[3] In the "chickie run" scene from the film Rebel Without a Cause, this happens when Buzz cannot escape from the car and dies in the crash.

The opposite scenario occurs in Footloose where Ren McCormack is stuck in his tractor and hence wins the game as they cannot play "chicken".

A similar event happens in two different games in the film The Heavenly Kid, when first Bobby, and then later Lenny become stuck in their cars and drive off a cliff.

The basic game-theoretic formulation of Chicken has no element of variable, potentially catastrophic, risk, and is also the contraction of a dynamic situation into a one-shot interaction.

The hawk–dove version of the game imagines two players (animals) contesting an indivisible resource who can choose between two strategies, one more escalated than the other.

The earliest presentation of a form of the Hawk–Dove game was by John Maynard Smith and George Price in their paper, "The logic of animal conflict".

[6] The traditional [4][7] payoff matrix for the Hawk–Dove game is given in Figure 3, where V is the value of the contested resource, and C is the cost of an escalated fight.

[7] Biologists have explored modified versions of classic Hawk–Dove game to investigate a number of biologically relevant factors.

In that film, the Russians sought to deter American attack by building a "doomsday machine", a device that would trigger world annihilation if Russia was hit by nuclear weapons or if any attempt were made to disarm it.

However, the Russians had planned to signal the deployment of the machine a few days after having set it up, which, because of an unfortunate course of events, turned out to be too late.

Either the pure, or mixed, Nash equilibria will be evolutionarily stable strategies depending upon whether uncorrelated asymmetries exist.

The line in graph on the left shows the optimum probability of playing the escalated strategy for player Y as a function of x.

The third Nash equilibrium is a mixed strategy which lies along the diagonal from the bottom left to top right corners.

If the players do not know which one of them is which, then the mixed Nash is an evolutionarily stable strategy (ESS), as play is confined to the bottom left to top right diagonal line.

Formal game theory is indifferent to whether this mixture is due to all players in a population choosing randomly between the two pure strategies (a range of possible instinctive reactions for a single situation) or whether the population is a polymorphic mixture of players dedicated to choosing a particular pure strategy(a single reaction differing from individual to individual).

Since neither player has an incentive to deviate from the drawn assignments, this probability distribution over the strategies is known as a correlated equilibrium of the game.

If no such uncorrelated asymmetry exists then both players must choose the same strategy, and the ESS will be the mixing Nash equilibrium.

[13] Replicator dynamics is a simple model of strategy change commonly used in evolutionary game theory.

The single population model presents a situation where no uncorrelated asymmetries exist, and so the best players can do is randomize their strategies.

War of attrition models a situation in which the outcomes differ only in degrees, such as a boxing match in which the contestants have to decide whether the ultimate prize of victory is worth the ongoing cost of deteriorating health and stamina.

The war of attrition seeks to answer the question of how contests may be resolved when there is no possibility of physical combat.

Both players accrue costs while displaying at each other, the contest ends when the individual making the lower bid quits.

Similarly, the prisoner's dilemma is a symmetrical 2x2 game with conflicting interests: the preferred outcome is to Defect while the opponent plays Cooperate.

This pretense continually moves forward past one project checkpoint to the next until feature integration begins or just before the functionality is actually due.

The psychological drivers underlining the "schedule chicken" behavior in many ways mimic the hawk–dove or snowdrift model of conflict.