1. Consider the following game:

Two teens engage in a game of Chicken, where they drive towards each other on a single-lane road and whoever swerves first loses the game and is labeled as a “chicken,” while the other gains social status. However, if neither player swerves, both will die in a fatal collision. The payoffs for the Chicken game are summarized in the table below.

The film A Beautiful Mind, which won an Academy Award, portrays John Nash’s contribution to game theory in a single scene. In the scene, Nash and his male graduate friends are at a bar where they notice a group of women, including one blond and several brunettes, and they agree that the blond is more desirable. Nash views the situation as a game of competing for the attention of the women among the male graduate students. The game is defined as follows: n male students simultaneously approach either the blond or one of the brunettes. If male i alone approaches the blond, he is guaranteed to get a date with her and earns a payoff of a. However, if one or more other males approach the blond along with i, the competition causes them all to lose her, and i, as well as the other males, earn a payoff of zero. On the other hand, male i earns a payoff of b > 0 if he approaches a brunette because there are more brunettes than males, meaning that i’s chances of getting a date with a brunette are higher. The blond’s higher desirability implies that a > b.