Why Learn HS Math? - Money and Game Theory

The complaint that I hear often from my students is “Why do I have to learn math???  It doesn’t have anything to do with real life!”  There is usually an increase of this belly-aching when it’s time to turn in homework or take a test.

There are several examples that I like to use.  Since I teach high school students, many of them are entering the workforce and beginning to experience the true value of money (earning, spending, and saving) for the first time.  With Christmas and New Year’s Day coming around, it seemed fitting to discuss the following scenario:

You’re working a full-time job that pays you $24,000/year.  Year-end bonus time comes around and your boss gives you the options of either getting a 4% raise for one year or receiving a bonus check for $2,000.  Which one would you pick?

Overwhelmingly, the students picked the 4% raise (even though they understood that the increase would only be for one year). When I asked them why? Most of them said that a raise “sounded better” than a lump sum payout. Really??? Turn on your calculators and find 4% of $24,000. Maybe it’s just me, but $960 does not seem better than $2,000. Not knowing how to apply math to a real-life problem resulted in a $1,040 loss.

A few days later, a different mathematical phenomenon unfolded right before our eyes – Game Theory.

According to the Stanford Encyclopedia of Philosophy, “game theory is the study of the ways in which strategic interactions among economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents.”  In essence, game theory is about trying to make the best choice when presented with a conflict where neither participant knows what the other will do. 

The definition of zero-sum game is a situation or interaction between two parties in which one participant’s gains result only from another’s equivalent losses – in other words, one player wins (+1) while the other one loses (-1).  The sum of the two values is zero.  The prisoner’s dilemma is one of the best known strategies in game theory.  It has been used to help us understand what makes people choose competition over cooperation when caught in a zero-sum game.

Anyway, back to the classroom.  I was grading tests when I found two papers that had identical answers.  It was obvious that one student had cheated off the other.  Unfortunately, without proof, I couldn’t penalize either one for breaking the code of honor.  So, I decided to try a little experiment.

I announced to the class that two people had been caught cheating.  The first person to confess would receive a warning, whereas the other would get a zero.  Some kids tried to rally behind the two offenders.  They played devil’s advocate by saying if no one confessed at all, there would be no case and the issue would probably be dropped.

Even though neither student knew what the other would pick, they did know – from my announcement – it would be in their best interest to confess; they wouldn’t completely get away with cheating but a warning would be better than a failing grade.

However, there was also the chance that by not confessing, they wouldn’t get a penalty at all, though that would be riskier… because they could instead fail.

Confessing is the “rational” choice.

But not confessing is acting with what’s called “rational irrationality.”

In the end, one student finally decided to come clean and confess to everything.  She couldn’t take the chance that her co-conspirator would break his resolve first and let her take the fall (especially since she was the one who actually studied for the test in the first place).

The next day, we had a very engaging discussion on game theory and life in our Geometry class. It’s funny how math has nothing to do with everyday life…

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