Game theory on reality television
ABC’s “Bachelor Pad” is a reality show that brings together 18 contestants from past “The Bachelor” and “The Bachelorette” seasons. It is usually enjoyed only as a guilty pleasure of mine, but in the finale last Monday, the final two contestants, Holly and Michael, were put in a Prisoner’s Dilemma-type situation that relates directly to our Game Theory section of class.
Host Chris Harrison presents the audience with how the $250,000 prize money is going to be divided, which Holly and Michael knew about beforehand. The audience is told that the two will go into separate rooms, and choose between two options, “SHARE” or “KEEP.”
– If they both pick “SHARE” they walk away with $125,000 each.
– If one chooses “SHARE” and the other chooses “KEEP”, the contestant that chose “KEEP” gets the entire $250,000.
– If they both choose “KEEP”, neither gets the money and it is split among the 16 other bachelors/bachelorettes that have already been eliminated, who are sitting and watching in the studio.
In this game, keeping is actually the dominant strategy:
– If Michael chooses keep, Holly gets the same amount whether she chose share or keep.
– If Michael chooses share, Holly has a higher payoff if she chose keep.
Because of symmetry, the same argument holds for Michael based on what Holly could choose.
So why would either contestant ever choose to share? Using only game theory, we could expect both players to have chosen keep. But in reality, the payoffs are not the only effect on the outcome of the game. The players may not necessarily decide to play the dominant strategy, or even play a Nash equilibrium, if there are outside influences on what choice to make. In the case of this reality show, Michael and Holly have a strong friendship with each other, and choosing to keep the money could lead to unfavorable consequences, such as the loss of a friendship.
This reminded me of our discussion in class about auctions where participants are colluding. If at least two people are working together to make a strategy in the game, then the natural rules of game theory begin to fall apart. Because Michael and Holly are friends, they can choose to “work together” to decide the outcome for this prize money. Being fair and splitting the money is a very reasonable outcome, especially when they have had the chance to discuss this situation before they made their choices. All they need to do is continue to trust each other while they are in the separate rooms, and not turn on the other person.
After much deliberation and many commercial breaks, it is revealed that both Holly and Michael both chose “SHARE”, and the money was split evenly between them.
http://www.hulu.com/watch/277615/bachelor-pad-week-6-part-2
http://www.entertainingeconomics.com/2011/09/bachelor-pad-game-theory.html
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