Prisoner's Dilemma: The Bank Job (and other alternatives)
November 13th, 2012 at 6:08:43 AM
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As the WoV Golden Balls Tournament is underway, it seems that Prisoner's Dilemma games have caught the interest of those on the board. Turns out, another British game show made use of it in a one-off series, with a twist that doesn't degenerate it into a paper/rock/scissors choice.
On series 1 of "The Bank Job", 5 finalists competed to win a jackpot that had been building all week. In the first 3 rounds of the finals, 3 of the 5 players were eliminated, leaving just two to go head-to-head in a Prisoner's Dilemma, for over 400,000 pounds. Called "Cash or Trash", each player gave a briefcase to their opponent. If they both gave each other cash, they split the jackpot. If one gave cash and the other gave trash, the lone player with the cash won the lot.
The twist: If they both gave each other trash, the three eliminated finalists split the jackpot. So instead of no one winning anything, there is a guaranteed payout.
Watch it play out here.
Want to see other examples of Prisoner's Dilemma in British game shows? Check these entries out.
And finally, a further twist on the concept. Can players split a jackpot between themselves, forced to divide it 60/30/10? Titled "The Most Uncomfortable 100 Seconds In Game Show History", see for yourself.
On series 1 of "The Bank Job", 5 finalists competed to win a jackpot that had been building all week. In the first 3 rounds of the finals, 3 of the 5 players were eliminated, leaving just two to go head-to-head in a Prisoner's Dilemma, for over 400,000 pounds. Called "Cash or Trash", each player gave a briefcase to their opponent. If they both gave each other cash, they split the jackpot. If one gave cash and the other gave trash, the lone player with the cash won the lot.
The twist: If they both gave each other trash, the three eliminated finalists split the jackpot. So instead of no one winning anything, there is a guaranteed payout.
Watch it play out here.
Want to see other examples of Prisoner's Dilemma in British game shows? Check these entries out.
And finally, a further twist on the concept. Can players split a jackpot between themselves, forced to divide it 60/30/10? Titled "The Most Uncomfortable 100 Seconds In Game Show History", see for yourself.
-Dween!
November 13th, 2012 at 6:50:55 AM
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http://www.youtube.com/watch?v=a8OO4NpMsD0
I just had to watch this again after all this back stabbing/greed.
I just had to watch this again after all this back stabbing/greed.
“Man Babes” #AxelFabulous
November 13th, 2012 at 7:47:29 AM
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Probability that the two remaining contestants give cash is denoted by p1 and p2.
So, the EV for the players are (in units of jackpot size):
EV1 = p2 * (1-p1) + p2 * p1 / 2.
EV2 = p1 * (1-p2) + p1 * p2 / 2.
Nash equilibrium is established, if everyone maximizes their EV, given that all players know each others strategies.
So player 1 maximizes EV1 with respect to p1 for any given p2, which means p1 = 0.
Likewise p2 = 0 for perfect symmetry.
Or in other words: You only win any money if the other person gives you cash. You always double the money given (or not given) to you if you give trash. So the Nash-equilibrium strategy is to always give trash.
As a result, the Nash equilibrium is the jackpot for the other contestants. If no communication between the contestants is possible, you probably should try to not advance to the next rounds.
So, the EV for the players are (in units of jackpot size):
EV1 = p2 * (1-p1) + p2 * p1 / 2.
EV2 = p1 * (1-p2) + p1 * p2 / 2.
Nash equilibrium is established, if everyone maximizes their EV, given that all players know each others strategies.
So player 1 maximizes EV1 with respect to p1 for any given p2, which means p1 = 0.
Likewise p2 = 0 for perfect symmetry.
Or in other words: You only win any money if the other person gives you cash. You always double the money given (or not given) to you if you give trash. So the Nash-equilibrium strategy is to always give trash.
As a result, the Nash equilibrium is the jackpot for the other contestants. If no communication between the contestants is possible, you probably should try to not advance to the next rounds.
November 13th, 2012 at 7:55:51 AM
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Quote: DweenWatch it play out here.
I predicted both would pass trash. Darragh because he couldn't make eye contact and often hung his head low, as in shame. Michael because he was begging the other person to "split." As I mentioned in another post, stealers put on a big show, trying to convince the other person to share the money.
"For with much wisdom comes much sorrow." -- Ecclesiastes 1:18 (NIV)
November 13th, 2012 at 8:40:20 AM
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Its not a true prisoner dilemma if a pair of steals results in a a better result than a co-op being stolen from.
"Then you can admire the real gambler, who has neither eaten, slept, thought nor lived, he has so smarted under the scourge of his martingale, so suffered on the rack of his desire for a coup at trente-et-quarante" - Honore de Balzac, 1829
November 13th, 2012 at 9:31:22 AM
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Quote: thecesspitIts not a true prisoner dilemma if a pair of steals results in a a better result than a co-op being stolen from.
I think a prisoner dilemma is, when the locally stable result is actually not the globally best result.
In this game there is no rational reason for the underperforming cooporation, because there are no further consequences.
Even if you "agree" to cooporate, chosing "trash" is your better option.
The best way would be to make a contract as a contestant, with penalty. It don't have to be written down to be legal.
November 13th, 2012 at 10:16:47 AM
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The thing is, though, if you know your opponent is going to steal, you're screwed either way. Traditionally, in the prisoner's dilemma, whatever your partner does, you're better off stealing. The fact that you're no better off both stealing than being stolen from is an incentive to share.
The trick to poker is learning not to beat yourself up for your mistakes too much, and certainly not too little, but just the right amount.
November 13th, 2012 at 10:21:59 AM
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Quote: MangoJI think a prisoner dilemma is, when the locally stable result is actually not the globally best result.
No, this is too general. My game theory book backs up the wikipedia article, which says that the payoffs all have to be different (and ordered in a specific way) to create the prisoner's dilemma.
Golden Balls is a variant, not a true prisoner's dilemma. In true prisoner's dilemma, 'defect' is dominant, while in Golden Balls, it is only weakly dominant. There is only 1 Nash Eq in prisoner's dilemma, but 3 in Golden Balls.
You are right that in both cases, the global EV maximizer is not Nash.
Wisdom is the quality that keeps you out of situations where you would otherwise need it
