Game Theory

Chicken Game

Chicken game is an often used application in game theory. It involves two cars on a single lane road, both cars are headed towards each other. A crash will be obvious, unless one (or both) driver swerves off the road and avoids a crash. However, this driver is then called the chicken and is the loser of the game. We can represent this game using game theory and a pay-off matrix.

If both players swerve, nothing has happened and both continue, we can give both of them a 0. If one strays of and the other stays on the road, we can give the ‘winner’ a 1 and the loser a 0. If both of them continue driving on the road and a crash happens, both of them lose heavier so we can give them a -10.

Which choice will be taken depends on the drivers. If one assumes the other will logically swerve off the road, he will then stay on the road and be the winner. However, the other driver will be thinking the same thing so we can say there are multiple Nash equilibriums. Here, there are three, all of them except the Straight/Straight combination.

The chicken game can be generalized to a general pay-off with the following relations.

b>d>c>a
y>z>x>w