Wednesday, September 15, 2010

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).


  1. Anonymous4:32 PM

    I'm not sure I agree with your assessment as to the reasoning the Nash Equilibrium was not reached. In a one-time game, eye-contact should not affect the outcome. In fact, if you wanted the entire prize to yourself, you would want to make that eye contact and then go ahead and choose "keep." I think a better explanation is that this game doesn't capture the entire payoff. That is, there is some downside in being on national television and being seen as greedy, whereas being seen as generous may well be worth more than the marginal 125k you are giving up. After all, reality show contestants are most skilled at marketing themselves - voting to take the money may "cost" way more in terms of future reputation.

  2. I think the eye contact at least reassures each player that the other is likely to "share" the money.

    As for the it being on TV, I definitely agree. As I mentioned, this doesn't take place in a private interrogation room, it takes place in front of millions of their peers.

  3. Anonymous6:33 PM

    Millions of people watch "Bachelor Pad"? There's a better reflection of scoiety.

  4. Ha ha, good point. That may be better proof that people are irrational.


    With the Bachelor Pad Finale out today, I thought I would give my prediction based on Economics and Game Theory.

    Assuming the set up is the same as last year, here is the decision that the winning couple has to make:

    it was the same exact ending as last season. Each player in the couple has to choose either “Keep” or “Share.”
    If one chose “Keep” and the other chose “Share”, the one who chose keep gets all 250k.
    If they both chose “Share”, they split the 250k.
    If they both chose “Keep”, neither gets anything, and the remaining 14 contestants split the 250k.

    There are two players in this game only, the remaining 14 contestants are not able to play this game. They simply get a reward as a result of the other players decisions.

    In an ordinary circumstance, this is a prisoners' dilemma game. Where the two players simultaneously choose an action:

    Cooperation would involve each player choosing "Share". Supposing that each player chooses share, given the other players' action as constant - each player has an incentive to deviate from his/her strategy. Basically, given that your partner chooses "Share", you would prefer to choose "Keep" rather than "Share" because you get 125k extra. Given that both players think this way, both players will choose "Keep" and end up receiving nothing.

    The Bachelor Pad game, however, is different.

    If they end up choosing Keep and seemingly greedy...the public persona of themselves will change. Of course, these contestants care hugely about the public opinion of themselves since they have appeared on Bachelor/Bachelorette and now Bachelor Pad.
    Even though they are greedy for fame, they can still be greedy for money. Even though they did not receive compensation for Bachelor/Bachelorette, they did for Bachelor Pad and many of these individuals/couples throw public stunts to sell their story to a magazine. (Vienna is said to have sold her break up story with Jake to a magazine before even telling Jake!)
    So which is more important to them fame or money? And surely they will still be famous having won Bachelor Pad anyway so, in that case, they can retain both fame and money.
    Lastly, and importantly, most of these couples are actual together (possibly in love?) so there is another cost to choosing "Keep" - their relationship with their partner.
    My opinion is that the bond of love/care is far greater than fame or money if it is genuine. So here are the couples and my prediction of the outcome if they reach the final:
    Ella and Kirk - They are not in love neither do they care deeply for one another. They have both expressed the intense desire to have the money. "Keep", "Keep" will be the result and neither will receive anything if they get into the final. A typical prisoner's dilemma outcome.
    Vienna and Kasey - It seems to me that Kasey's love for Vienna is far greater than that of Vienna. I predict that Kasey will choose "Share" and Vienna will choose "Keep" and walk away with the 250k having lost her relationship. However, Kasey is a schemer and has the capability to deceive, he might surprise us if we get to this stage.
    Michelle and Graham - they are starting to be in a relationship...I don't think they feel strongly enough for each other to choose "Share"...this could go either way.
    Michael and Holly - "Share", "Share". I predict they will split the 250k evenly. Even though they are not together any more and Michael is annoyed about her relationship with Blake - they care so much for each other. I can tell because Holly sent Blake home to spare Michael's feelings (well at least from that point on) and Michael is still in love with Holly. This is true love.
    What are your thoughts?


You are the reason why I do not write privately. I would love to hear your thoughts, whether you agree or not.