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Carol and Claire have just graduated from high school and they are appointed by their parents to run the business in a restaurant.
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Ha llegado la hora de pagar. Another example, taken from fiction, is found in Stanley Kubrick 's Dr. 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.
Players may also make non-binding threats to not swerve. This has been modeled explicitly in the Hawk—Dove game. All anti-coordination games have three Nash equilibria.
Two of these are pure contingent strategy profiles, in which each player plays one of the pair of strategies, and the other player chooses the opposite strategy.
The third one is a mixed equilibrium, in which each player probabilistically chooses between the two pure strategies. Either the pure, or mixed, Nash equilibria will be evolutionarily stable strategies depending upon whether uncorrelated asymmetries exist.
The best response mapping for all 2x2 anti-coordination games is shown in Figure 5. The variables x and y in Figure 5 are the probabilities of playing the escalated strategy "Hawk" or "Don't swerve" for players X and Y respectively.
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 line in the second graph shows the optimum probability of playing the escalated strategy for player X as a function of y the axes have not been rotated, so the dependent variable is plotted on the abscissa , and the independent variable is plotted on the ordinate.
The Nash equilibria are where the players' correspondences agree, i. These are shown with points in the right hand graph.
The best response mappings agree i. The first two Nash equilibria are in the top left and bottom right corners, where one player chooses one strategy, the other player chooses the opposite strategy.
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.
Otherwise an uncorrelated asymmetry is said to exist, and the corner Nash equilibria are ESSes. The ESS for the Hawk—Dove game is a mixed strategy.
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.
Biologically, these two options are strikingly different ideas. The Hawk—Dove game has been used as a basis for evolutionary simulations to explore which of these two modes of mixing ought to predominate in reality.
This mixed strategy equilibrium is often sub-optimal—both players would do better if they could coordinate their actions in some way.
This observation has been made independently in two different contexts, with almost identical results.
Consider the version of "Chicken" pictured in Figure 6. Like all forms of the game, there are three Nash equilibria. The two pure strategy Nash equilibria are D , C and C , D.
Now consider a third party or some natural event that draws one of three cards labeled: C , C , D , C , and C , D.
This exogenous draw event is assumed to be uniformly at random over the 3 outcomes. After drawing the card the third party informs the players of the strategy assigned to them on the card but not the strategy assigned to their opponent.
Suppose a player is assigned D , they would not want to deviate supposing the other player played their assigned strategy since they will get 7 the highest payoff possible.
Suppose a player is assigned C. So, the player would prefer to chicken out. 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.
Although there are three Nash equilibria in the Hawk—Dove game, the one which emerges as the evolutionarily stable strategy ESS depends upon the existence of any uncorrelated asymmetry in the game in the sense of anti-coordination games.
In order for row players to choose one strategy and column players the other, the players must be able to distinguish which role column or row player they have.
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