Wednesday, April 25, 2012

Game theory on TV

One of my regular non-poker reads is a blog called "The Agitator," by Radley Balko. He posted this YouTube clip today. It's brilliant. I've never heard of this game show before (I assume it's shown in Britain), but you don't need to know the rules, the host explains enough. Watch now if you're going to, because spoilers will follow.


 

 Of course, the problem presented to the contestants is just a minor variation on the age-old "Prisoner's Dilemma." But I love, love, love how the guy on the right solves it. He presents an utterly convincing case that he is going to steal, and therefore the only way that the guy on the left has any chance of getting half of the money is by selecting "share," trusting that Mr. Right will be as good as his word and split the money after the show. This is perfectly plausible to Mr. Left, because he can't think of any reason that Right would be lying about which ball he is going to select (though of course he might be lying about his post-show intentions). But in fact, the whole song-and-dance was just a ruse to manipulate Left into picking "share." It was Right's way of making sure that Left didn't try to steal. Right had me completely convinced. I was stunned when he revealed "share." It took me a few seconds to process what had happened, but then when I got it, I wanted to tip my hat to him for a stunning piece of applied game theory. Absolutely perfect!

You know that poker concept of thinking one level deeper than your opponent? Well, my hunch is that the guy on the right would be one fearsome player.

8 comments:

geezer said...

Brillant

snevman said...

Well played sir.

Peja Stojakovic said...

I feel like I live in an alien world. Both players made the wrong choice, largely based on an unenforceable promise. But it sure made for good TV.

Peja Stojakovic said...

I feel like I live in an alien world. Both players made the wrong choice, largely on the basis of the unenforceable promise of the player on the right.

Missingflops said...

Allowing for communication between the "prisoners" makes for a nice twist to the dilemma. I think it's interesting because IMO the "correct" answer to the traditional posing of the dilemma is to defect (or steal in this case) because when you defect you are maximizing your result independent of what the other "player" does although you are eliminating the chance for the result where everyone does best.

In this game there is less disincentive against stealing because the "bad thing" that happens if both players steal is a simple return to status quo so stealing is never worse than neutral EV. So I think the player that promised to steal figured an elegant solution to try and ensure the other player would pick split. Initially I thought that him not following through on his promise was an error as the strategy of lying about stealing could still be exploited. So if the other player "levels" and concludes he is being manipulated to choose split he could then conclude the first player is trying to force a split and steal.

The counter argument though is that by promising to steal and then splitting, Player A ensures that someone will get the money besides the house and then he can hope that Player B will voluntarily split later. You could almost look at it like a three player game where the third player is the show itself.

Not bad for a tv game show!

Marc said...

i'm not sure if you're familiar with the younger online players, but a girl named liv boree who now is part of team pokerstars played on this before she played poker about 6 years ago and tricked the other guys out and stole his money, haha. google/youtube it, it's pretty funny.

Rakewell said...

Of course I know who Liv Boeree is, but no, I didn't know she had been on this show.

Here's the clip:

http://www.youtube.com/watch?v=y6GhbT-zEfc

The other guy accuses her of having no integrity. He doesn't seem to understand that what is a perfectly fair and honorable tactic as allowed by the rules, within the confines of a game, is quite different from what may be fair and honorable in life outside the game. (This is something that players on reality shows such as Survivor also routinely fail to comprehend.) When the game requires deception in order to do maximally well (as is the case here), nobody should be shocked when players use deception.

James Antill said...

> I think it's interesting because IMO the "correct" answer
> to the traditional posing of the dilemma is to defect
> (or steal in this case) because when you defect you are
> maximizing your result independent of what the other
> "player" does although you are eliminating the chance
> for the result where everyone does best.

All the evidence from iterated PD tournaments would suggest this "solution" is far from optimal.

> In this game there is less disincentive against stealing
> because the "bad thing" that happens if both players
> steal
> is a simple return to status quo so stealing is never
> worse than neutral EV.

It's true that defect/defect has the same negative for you as coop/defect ... so it isn't a true "generalized form of PD". But it's not "neutral EV" to not win, when you could have won.