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June 12, Retrieved July 29, Gerhardt and Connor made a beautiful triple play in the sixth, retiring Start and Daily at second and first on a liner from Irwin 's bat.

Retrieved July 23, — via YouTube. Spokane Chronicle. Spokane, Washington. June 28, Retrieved July 30, — via newspapers.

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Namespaces Article Talk. Views Read Edit View history. A similar event happens in two different games in the film The Heavenly Kid , when first Bobby, 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.

If both players choose the Hawk strategy, then they fight until one is injured and the other wins. If only one player chooses Hawk, then this player defeats the Dove player.

If both players play Dove, there is a tie, and each player receives a payoff lower than the profit of a hawk defeating a dove.

A formal version of the game of Chicken has been the subject of serious research in game theory. In Figure 1, the outcomes are represented in words, where each player would prefer to win over tying, prefer to tie over losing, and prefer to lose over crashing.

Figure 2 presents arbitrarily set numerical payoffs which theoretically conform to this situation. Here, the benefit of winning is 1, the cost of losing is -1, and the cost of crashing is Both Chicken and Hawk—Dove are anti-coordination games , in which it is mutually beneficial for the players to play different strategies.

In this way, it can be thought of as the opposite of a coordination game , where playing the same strategy Pareto dominates playing different strategies.

The underlying concept is that players use a shared resource. In coordination games, sharing the resource creates a benefit for all: the resource is non-rivalrous , and the shared usage creates positive externalities.

In anti-coordination games the resource is rivalrous but non-excludable and sharing comes at a cost or negative externality.

Because the loss of swerving is so trivial compared to the crash that occurs if nobody swerves, the reasonable strategy would seem to be to swerve before a crash is likely.

Yet, knowing this, if one believes one's opponent to be reasonable, one may well decide not to swerve at all, in the belief that they will be reasonable and decide to swerve, leaving the other player the winner.

This unstable situation can be formalized by saying there is more than one Nash equilibrium , which is a pair of strategies for which neither player gains by changing their own strategy while the other stays the same.

In this case, the pure strategy equilibria are the two situations wherein one player swerves while the other does not.

In the biological literature , this game is known as Hawk—Dove. It is almost always assumed that the value of the resource is less than the cost of a fight, i.

The exact value of the Dove vs. Dove payoff varies between model formulations. Biologists have explored modified versions of classic Hawk—Dove game to investigate a number of biologically relevant factors.

These include adding variation in resource holding potential , and differences in the value of winning to the different players, [9] allowing the players to threaten each other before choosing moves in the game, [10] and extending the interaction to two plays of the game.

One tactic in the game is for one party to signal their intentions convincingly before the game begins. For example, if one party were to ostentatiously disable their steering wheel just before the match, the other party would be compelled to swerve.

One real-world example is a protester who handcuffs themselves to an object, so that no threat can be made which would compel them to move since they cannot move.

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.