Bachelor Pad Game Theory

In case you missed it, the first season of The Bachelor Pad just ended. It is a Survivor-style reality TV show on ABC. It features losing contestants from previous seasons of The Bachelor and The Bachelorette competing for $250,000. Every week a series of dates, challenges, and votes determined who would stay and who would go. This week it was narrowed down to a final "couple", Dave and Natalie. The winner between the two of them was to be determined by a psychological experiment.

Dave and Natalie were forced to go into separate rooms and decide whether they wanted to "keep" or "share" the final prize. If they both picked “share”, the money would be split evenly between them ($125,000 each). If only one picked “share” and the other "keep”, the keeper gets the entire prize ($250,000) and the other, we'll call them the weeper, gets nothing. If they both pick "keep", then neither gets the cash and it is split among the other losing contestants (about $14,000 each). Sound familiar? It should. It's the famous Prisoner's Dilemma.

Here's how the experiment is usually described. Two criminals are arrested without much evidence and so are put in separate rooms. Each prisoner is offered the same deal that if they confess before their partner in crime does, they will receive no punishment and the other will go to jail. If they both confess they will both go to jail. However, because there is not much evidence, if neither confesses, there is only a small punishment. In this situation, how should the prisoners act? Or back to our original story, what should Dave and Natalie do? A little game theory, or strategy accounting for others' strategy, should help:

As the matrix above shows, red player's best choice, no matter what the blue player does, is always to defect. The same is true for the blue player. So in our reality TV example, no matter what Dave chooses, Natalie is best off is she chooses to "keep" the money. The same is true for Dave. So did they act like the completely rational, completely self-interested, Homo economicus? No. In fact, both Dave and Natalie chose to split the money. I must admit, I would not have predicted that. However, I think I can explain why.

In the original Prisoner's Dilemma, the offer is made while both are separated. On the Bachelor Pad, the rules were explained while both contestants were sitting next to each other. Immediately they both made eye contact, as if to reassure each other of their relationship. If they were not allowed that moment, I'm not so sure the outcome would have been the same. Also, the original game takes place in a private interrogation room. The Bachelor Pad finale was watched by millions. Sometimes money isn't the only cost calculated. Overall show quality aside, it made for a pretty good ten minutes of television (watch here).

Hat tip to Lessons Learned Over Dinner (earlier).