Game Theory: The Game of Chicken

By Mary Jane Sterling

Finite math applies many basic mathematical processes to real-world problems. For example, have you ever been called a “chicken” for not being willing to jump off the diving board or stick your finger in the hot cocoa? You probably didn’t realize that this is a classic in game theory and has been immortalized in the movie Rebel without a Cause.

A basic illustration of the game of chicken is having two cars on a deserted road, heading directly at one another. Whoever swerves out of the way is deemed a chicken. And, yes, you know the other consequences. The following shows the results of the game in terms of the results for R.

FNTMATH_1401

And how do you put this into a game payoff matrix? With the payoffs in terms of R, the following would work. Note the value of the crash!

FNTMATH_1402

The lowest value in the first row is the highest value in that column, so that would be the saddle point. Also, the second column dominates the first column, so you would adjust the matrix to a column matrix, where the first row is still the best choice.

A row dominates another row if every entry in the row is larger than the corresponding entry in the other row. But a column dominates if its corresponding entries are all smaller than those in the other column.

What happened in Rebel without a Cause? The characters play a game of chicken when they steal cars and drive them off a seaside cliff. The idea was that you’re a chicken if you jump out of the car unless it’s just about to go over the cliff. In the movie, one of the characters tries to jump out, but his jacket gets caught on the door, so he goes over, anyway. Also, an even sadder note is that the star, James Dean, later died in a car crash at the age of 24.