Game Shows And Game Theory
There's a British game show called Golden Balls in which two contestants play a game similar to the Prisoner's Dilemma. The prize of the pot varies by week but each contestant can choose whether to split the pot or steal the pot. They're given two balls, one says steal, one says split. If both choose to "split," they split. If both choose to "steal," they get nothing. And if one chooses "steal," he wins the whole pot and the other player, who chose "split," gets nothing.
What makes this different from a classic Prisoner's Dilemma is that prior to making their pick, they get a few minutes to talk to each other and make claims about what they're going to do.
First, let's see this in action:
Now, I have another video I want to show you featuring another episode of this show. But before I do that, I am very curious to find out what your strategy would be if you played this game.
- Comment (47)
- · Quote
- · UnfollowFollow (8)
Comments:
Jan '11
Re: Game Shows And Game Theory
Standard game theory ...
In a one-shot iteration of a PD, you choose non-cooperation.
If the game is indefinitely iterated (repeated a number of times unknown to the players) then you adopt a strategy. Robert Axelrod wrote a foundational textbook on what strategy to choose, called the Evolution of Cooperation. In a computer-staged tournament, Axelrod compared a host of strategies. The winner was Tit-for-Tat; meaning, you begin by cooperating, and then you do whatever your opponent did in the previous game.
It also prompted the great line from a fellow classmate ..."What's a tat, and where can I go to exchange it?"
Apr '11
Re: Game Shows And Game Theory
...
And that's why you always have to focus on rationality when a pretty gal gives you the pouty face.
Oct '10
Re: Game Shows And Game Theory
But it's not standard game theory...they are making the decision in front of an audience, face to face with the other person. So, there is an element of not wanting to look bad, and there is an element of being able to act well.
I couldn't pull off what that woman pulled off, just in terms of her performance, so I would have to cooperate.
My guess is that most people on average would cooperate, but that the producers seek out contestants that might be willing to defect and are able to pull it off.
Edited on April 20, 2012 at 7:47pmAug '10
Re: Game Shows And Game Theory
The incentive to steal is even greater for this scenario than for the classic prisoner's dilemma.
After all, the contestants in this game are already competitors, not colleagues. There is no reason to trust the other person. So clearly, the best strategy is to try to sweet-talk the other competitor and then pick steal, just like the woman in the clip.
In the classic prisoner's dilemma, the two prisoners are colleagues. Therefore, there's more reason for each one to think that the other might act cooperatively.
Apr '11
Re: Game Shows And Game Theory
Misthiocracy: The incentive to steal is evengreater for this scenario than for the classic prisoner's dilemma.
After all, the contestants in this game are alreadycompetitors, not colleagues. There isnoreason to trust the other person. So clearly, the best strategy is to try to sweet-talk the other competitor and then pick steal, just like the woman in the clip.
In the classic prisoner's dilemma, the two prisoners are colleagues. Therefore, there's more reason for each one to think that the other might act cooperatively.
Exactly. The essential question here is: How much do you trust the other person?
When I was in Middle School, our youth pastor gave us a similar game, War and Peace. We were in four teams, each team had a diplomat and a president. If we all declared Peace, we'd all get 4000 points; War we'd all get -4000 points. If it was split, we got varying values, with those declaring War getting points and Peace losing.
Needless to say, despite the diplomats all agreeing Peace most advantageous to all, every team individually decided War would get them ahead.
I'd trust no one on this show.
Aug '10
Re: Game Shows And Game Theory
There's also the element that some people are better at "reading" non-verbal cues and body language than others.
Someone trained in spotting the non-verbal cues of a liar is going to perform better than someone who isn't trained.
There's also the element of being able to analyse your opponent's arguments.
In the clip, the man is explaining to the girl why he could never choose steal, because he's afraid of what people would think of him. He assumes that her default position is not not trust him, so he tries to convince her that he's trust-worthy.
The girl, on the other hand, pleads with him not to cheat her. She assumes that his default position is to trust her, so she builds on that by appealing to HIS sense of honesty.
He loses because he gives her more information than she gives him.
Jan '11
Re: Game Shows And Game Theory
I know nothing about this game show ... is it always a one-shot game, or is there ever a series?
The fun is in a series against multiple opponents.
Dec '11
Re: Game Shows And Game Theory
Called It!
While it is a bit different from the PD (more up close and personal) it still does come down to the same thing: predict what the other person will do, then act accordingly. Once that guy played his hand, the girl had two choices: settle for 50,000, or take it all.
Apr '11
Re: Game Shows And Game Theory
Essentially as there's a talk session, there's a power play being made. The trick is to make the conversation be about the other guy, never about you. The entire time the contestants were talking, it was always about what the gent was doing. Even though he assured her he was going to pick Split, he never gained similar assurances from her. She maintained the power position the entire conversation.
Aug '10
Re: Game Shows And Game Theory
Furthermore...
Let's assume that they're both are basically decent people who share similar values of basic ethics and morality. After all, psychopaths and other ethical deviants are statistically rare.
Now, he promises that he won't steal. If he breaks his promise and steals, that means he's a liar.
Therefore, he has more to lose, conscience and reputation-wise. For him to go back on his promise would require that he willfully go against his own conscience and ethical beliefs, and risk being forever known as a liar.
She, on the other hand, never actually says that she won't steal. If she steals, she isn't a liar, which makes a big difference psychologically.
For her to steal does not require a willful effort to go against her conscience, because she took the time to set up the ethical conditions specifically to justify her choice. After all, she can honestly say that she never told him she wouldn't steal.
Re: Game Shows And Game Theory
Technically, this is not the classic PD. In the classic PD, you are worse off if you split and the other person steals than if both steal. Here, you get 0 in both cases. Imagine that the two players have to pay an entry fee of, say, $1000 to play. If both steal, both get their entry fee back. But if you split and your rival steals, you get no prize and forfeit your entry fee. Would it make a difference?
I've staged this game, that is, the proper PD, (with as much pre-play communication as the participants desire) with many generations of Stanford MBAs and Exec Ed participants. Even in a one-shot game, they cooperate (split) at least 80% of the time, because they have to live with the "reputation" this creates. (Also, the stakes are much, much lower.) Repeated play gets more cooperation. But the killer is a variation where there is repeated play (same two people play over and over, with an indefinite final stage) with noise---there is a small chance that what you want to play is not what you do play. It makes for some fascinating conversations and dynamics.
Aug '10
Re: Game Shows And Game Theory
Question:
Does anybody know if this show has been on the air for very long?
I'm betting that it has not, because it would not take very long for reasonably intelligent people to watch enough episodes to figure out the most likely strategies and tactics, and if you get contestants who have any knowledge of game theory then forget it.
It's sorta like Deal Or No Deal. That show is no longer on the air at least in part because the mathematical trick for beating the game became too well-known.
Feb '11
Re: Game Shows And Game Theory
Where's the pistol? That's the one prop they're missing. Then it could be steal/split, loaded/unloaded.
Edited on April 20, 2012 at 8:37pmRe: Game Shows And Game Theory
Another variation is the centipede game. Start with a stack of 100 $1 bills (or, if you have a rich patron, 100 $20 bills, or $100 bills). One bill is put on the table and the first participant can "wait" or "take." If she waits, another bill is put on the table and the other participate can "wait" or "take." If he "waits," a third bill is put on the table and she chooses again, and so forth. If ever someone "takes," that person gets everything on the table, and the game is over. On the final turn (when the last bill is put on the table), the second participant chooses between "take it all" or "split." Clearly, both players want to "wait" for a while, so that the stakes build up. But suppose there are, say, 90 bills on the table. The end is near. Will you "wait" or "take"?
This adds a lot of nonverbal communication: What would you do if, say, there were 70 bills on the table, and your rival just took a long time deciding whether to take or wait and finally said "wait"?
Jun '10
Re: Game Shows And Game Theory
My strategy would be to inform my opponent that I intend to "steal" the pot, but that I will share it with him if he opts to play "split." My opponent would be forced into a situation where his only way to win would be to trust me. If he chooses to deny me, then he also denies himself.
Aug '10
Re: Game Shows And Game Theory
As soon as one person chooses that strategy, they pretty much have to cancel the television show.
Edited on April 20, 2012 at 8:44pmRe: Game Shows And Game Theory
KC Mulville: I know nothing about this game show ... is it always a one-shot game, or is there ever a series?
The fun is in a series against multiple opponents. · 2 minutes ago
I believe they each play against each other repeatedly on their way to the final round -- so they get a feel for how trustworthy the other is.
Re: Game Shows And Game Theory
Misthiocracy: Question:
Does anybody know if this show has been on the air for very long?
I'm betting that it has not, because it would not take very long for reasonably intelligent people to watch enough episodes to figure out the most likely strategies and tactics, and if you get contestants who have any knowledge of game theory then forget it.
It's sorta like Deal Or No Deal. That show is no longer on the air at least in part because the mathematical trick for beating the game became too well-known. · 15 minutes ago
I'm trying to hold off on posting the second video until a few more people weigh in but it's related to what you say!
Re: Game Shows And Game Theory
Based on that video, it's very apparent that guy doesn't have any steel balls.
Jul '11
Re: Game Shows And Game Theory
You tell the other person ahead of time that they either pick the split ball ( as will you) or you send a pipe hitting man to their house and they never walk again. The rest of the world is so silly to not think of such an easy solution.