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Playing "Chicken" - Equilibrium Analysis

4. Some foolish teenagers play "chicken" on Friday nights. Two teenagers drive their cars at each other at high speeds. The first to swerve to the side is the "chicken" and loses. If both swerve out of the way, they are both chickens and both lose. Neither of the drivers wants to get into an accident. It causes a significant loss in utility (possibly death). However, both do not want to be known as a chicken. this causes some loss in utility. What is the equilibrium of this game? Do you think the two drivers will necessarily produce an equilibrium outcome? Do you think the chances are better or worse for achieving an equilibrium outcome if the two players know each other? Explain. Do you think it matters whether the two players have played the game before? Explain.

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These are the possible different strategies:

Player A swerves Player B swerves --> both lose some utility
Player A stays Player B swerves --> Player B loses some utility
Player A swerves Player B stays --> Player A loses some utility
Player A stays Player B stays --> both lose significant utility

There are two Nash equilibria, where one player stays and one swerves.

The two players have a big stake in guessing what the other will do. In this game, both players want to do the ...