The Prisoner's Dilemma Makes a Reality TV Appearance

Once in a while, something happens in the real world that brings a flurry of e-mail to the Freakonomics office. If, for instance, the Prisoner’s Dilemma, or at least a version thereof, makes an appearance on a network TV show.

The recent season finale of ABC’s reality show The Bachelor Pad featured an interesting twist. When it came time to award the show’s final $250,000 prize, the two finalists, 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).”

Wondering what happened? Take a look:

Harrison Brookie points to a few important differences between the standard prisoner’s dilemma and the reality TV version: “[T]he 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 … Also, the original game takes place in a private interrogation room.”

(HT: Jamie Nopper, Levi Funk, and a few others – thanks!)


Matt

Another important distinctive in this case is the awareness of the contestants of the possible impact of their decisions on the "brand value" accumulated by their participation up to that point in the media event. There was more at stake than one relationship and cash.

Raymond

Wasn't there a game show that did the Prisoner's Dilemma regularly at the end of the show?

Chap

This is almost exactly the same scenario as described in "The Art of Strategy" by Dixit and Nalebuff, where they reference the TV show Friend vs Foe. Their comment was that a surprising amount of contestants did what Dave and Natalie did too.

Richard Hawkins

I like this one
http://www.youtube.com/watch?v=p3Uos2fzIJ0
better

Matt Bruce

Have people already forgotten the game show Friend or Foe? Hosted by Kennedy (the former MTV VJ)!

Jimmy

The decision matrix was completely even from a dollar perspective, which made it a lot less interesting. To normal people, the difference between 0 and 125K is a lot more than 125K to 250K. On top of that, there was the actual relationship between them to consider, which made the share decision really, really easy.

They should have made the individual payoff a lot higher ($1 million) as to really tempt them and the mutual destruction much worse. So something like:

Two "SHARE" => $75K for each contestant.
One "SHARE", One "KEEP" => $1 Million for the "KEEP" contestant
Two "KEEP" => nothing for either of them.

That would be a far more interesting decision.

Cheez

According to the prisonner's dilemma, the betrayal strategy strictly dominates the cooperation strategy, i.e. no matter what the other player decides to do, you maximize your outcome by betraying.

However, in this case, if player 1 decides to keep the money (betraying player 2), then player 2 is indifferent between sharing and keeping, since he doesn't get any money anyway. He may even be more pleased to see player 1 leaving with the money instead of giving money to all the other contestants...

Brandon

Another big difference is that with the nature of their pre-existing relationship, and because there is only reward at stake as opposed to punishment, they might each rather the other person gets the money than neither of them.

As in, even if he assumes she will choose keep, he still chooses share because he would prefer she gets the money instead of the remaining competitors. And vice versa. Voila, they both share.

di

Was there anything stopping the Keeper to split it with the Weeper the next day, off camera? Just one more thing to think about.

Ian Kemmish

The betrayee can presumably also make more than $250,000 by selling his or her story to a "celebrity" magazine.

KevinM

Of course, it depends on whether The Bachelor Pad is a show or a series; also whether it's really a season finale or a show finale.

nobody.really

They should have made the individual payoff a lot higher ($1 million) as to really tempt them and the mutual destruction much worse. So something like:

Two "SHARE" => $75K for each contestant.
One "SHARE", One "KEEP" => $1 Million for the "KEEP" contestant
Two "KEEP" => nothing for either of them.

That would be a far more interesting decision.

I suspect it wouldn't. Instead, one player would look at the other and say; "You say Keep; I'll say Share; we'll split the $1 million 50/50 when we're done, ok?" Since this strategy would benefit both parties more than if they both said Share, I'd expect everyone would adopt it. The drama would then arise AFTER the show was over, to see if the winner honored the commitment to share the winnings.

I recall a similar game I played in my church youth group, called Feast and Famine. It would involve ten players and ten rounds. If each player submitted (confidentially) a Feast card, all players would win a point. If all players submitted a Famine card, all players would lose a point. If some submitted Feast and some submitted Famine, then the players that submitted Feast would lose a point and the players that submitted Famine would win a point. Clearly there's an incentive to cooperate, as well as an incentive betray the cooperative effort.

I looked on this as a game theory problem. I announced that getting all 10 players to cooperate anonymously would be very hard, but we could achieve nearly as good an outcome by a different strategy that would be much easier to implement. We'd ask everyone to turn in a Famine card EXCEPT ONE PLAYER - and we'd take turns being the one player that turned in the Feast card. In this scenario, all players but one would win a point each round. And because for each turn we knew whose turn it was to submit the Feast card, if we all lost points during that round we'd know who had betrayed us.

Ok, perhaps I missed the point of church youth group -- but I did understand game theory!

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Edward

Another point not emphasized in the show is that the decision is very public, which strongly biases decisions in the direction of sharing.

Imagine how awkward it would be for one of them in trying to form future relationships if people kept recognizing them: "Hey aren't you the jerk who chose to take all the money on that TV show?" Honestly, a lot of people would understandably have a hard time accepting that kind of notoriety just for $125,000.

KevinH

I wonder which aspect provided more social pressure to share: revealing in front of an audience and cameras, or revealing your choice in front of the other specific party.

It would be hard to do a study with as big of an audience as the show, but might be interesting way to quantify personal relationships!

Also, the woman would probably make a good poker player.

Chris Blalock

@di Why not just do it on camera in the first place? If the other person chooses to keep it, you won't have the opportunity to do so, regardless of your own choice. If the other person chooses to share it, you choosing to share it has the same outcome as choosing to keep it, assuming you actually follow through and split it evenly (besides the double taxation, of course).

--Lia

@7 Cheez-- The best long term strategy is not always to betray (or defect which is the word I prefer). The best strategy is tit-for-tat in which each player cooperates or defects according to what the last player has done in his/her last playing of the game. If the last time you played your opponent cooperated, then cooperate. If the last time you played your opponent defected, then defect. It yields the best long term results.

Slave Rat

Isn't the payoff for mutual betrayal in the classic prisoner's dilemma higher than zero?

A.J. Venter

In the end there is another factor. From reaching the final we can assume that both have a fair measure of skill at tactical decision making.
That means at least some skill at risk assesment.

The choice to keep is here clearly the highest potential risk factor. As you stand in there -you know that if you choose keep - you risk neither of you getting anything- and you guarantee you won't get to have a future relationship.

If the other person chooses keep, and you choose not end the relationship as a result, you can expect to get at least some of the benefit.

So sharing was clearly by a huge margin the lowest risk decision for both to make. Both of them knowing this- it was the obvious choice, and both also knew that the other knew- and they could reasonably expect the other to reach the same conclusion.

Essentially the differences from the classic prisoners dilemma here made the decision much easier than it would be in the classic case - and thus much more predictable.

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Spooner

Why is this post anonymous? (Oh, wait. Is there a Mr. Freakonomics?) Why is this called "reality TV"? It's just a game show. Anyone who thinks it to be "real" probably also believes pro wrestling and the tooth fairy are real. Natalie was hamming it up at the end, making the audience think she had chosen "keep". It was obvious that she had been directed.

Ms Toronto

An interesting decision and I agree that their eye contact would have got their message across of reassurance.