Introduction
Rational People; Irrational Behavior
I mentioned in the acknowledgments that for years I was puzzled by the seemingly irrational behavior of rational people going through a divorce, until I discovered game theory. I also mentioned in the acknowledgments the prisoner’s dilemma, the example that Steve Seaman showed me on a napkin. This example is presented in many versions, but the basic idea is as follows:
The Prisoner’s Dilemma Example:
Two crooks commit an armed robbery, but had masks on and would not be able to be identified, if caught. They also managed to hide the money they had stolen. However, the police caught them, with their weapons on them. Because they had criminal records, matched the general description of the robbers, and had guns on them, the police were pretty sure they were the perpetrators but needed more evidence to convict them. The police put the two suspects in separate rooms. The interrogator said the same thing to both men. He said, “We know you and your partner committed the crime. However, it is unlikely that we are going to be able to prove it. However, you are convicted felons caught with guns on you. That will get you three years of prison time. However, I am prepared to offer you a deal. If you confess and serve as a witness against your partner, we will recommend that you only serve one year and then are paroled, because of your cooperation. Your partner, who does not cooperate, will get seven years.”
The astute suspects asked, “But what happens if we both confess?”
The interrogator went on, “If you both confess, we will recommend that you only serve five of the seven years.”
Game theory gives us a specific approach to analyzing choices in a grid. This is an analysis of what is called a “simultaneous choice game,” because each of the players has to make a choice not knowing what the other player is choosing. We will present more on this in
Chapter 1.
In our grid, this is the deal that is being offered to the suspects:
Prisoner’s Dilemma
Examining the grid, we see that prisoner 1 gets three years if he stays silent and his partner stays silent, but he get only one year if he confesses. Thus, he does better to confess. If prisoner 2 confesses, he gets seven years if he stays silent but only five years if he confesses too. Thus, no matter what prisoner 2 does, prisoner 1 does better to confess. Prisoner 2 faces the same choices. Therefore he, too, does better to confess, no matter what prisoner 1 does. The rational choice for both prisoners, then, is to confess, but as can be seen, they would have both done better had they both remained silent. They made the rational choice, but it looks irrational because they made a self-defeating choice.
The Auction Example:
There is another famous experiment done with audiences during presentations on game theory. It is an auction. The presenter holds up a $100 bill and announces that he is auctioning it off to the highest bidder, but there is one twist in the rules. The second highest bidder also has to submit his or her bid, but does not get the $100 bill. The auction begins. Before long, the presenter has bids well over $100, sometimes close to $300. Why on earth would someone bid over $100 for $100. That seems totally irrational. But is it? Let us explain.
What happens is that the experiment quickly becomes a bidding war between two people. On the surface, i
