The Prisoner’s Dating Game
An extensive form representation of a prisoner...
An extensive form representation of a prisoner’s dilemma with an outside option for player 1 (Photo credit: Wikipedia)

A while ago, I dreamt that I was talking to a cute sort of indie-rock type girl on a bus, and she was working on a game show.  I didn’t actually get to see any of the game show — it was just told to me, and I pieced together the rules from her conversation. Basically, it was a version of The Dating Game, only a bit different. In this version[1], basically, as normal, the guy would ask the 3 women questions about whatnot, and would choose one for a “date” and go off on a trip, etc. In this one, however, the bachelor[2] was guaranteed the prize (considering how in the original the Bachelor couldn’t just go “thanks but no thanks, I’m leaving”, and walk out with nothing. Nor, would he probably want to, since a trip with a loathsome person is still a trip, and presumably you wouldn’t have to spend all your time with them and go off and do cool things while the other person stayed inside or did other cool things separate from you or whatever.); in this show, he had an extra option — if he didn’t like any of the women, he could choose to go with his sister.[3] In this eventuality, though, the Bachelorettes would win, say, 5000 dollars (in the dream, the trip was worth $20,000). But if the guy chose one of the non-sister ladies, the un-chosen ones would get Zippo. Or, rather, a lifetime supply of Rice-a-Roni, the San Francisco Treat.[4]

Basically, it’s the Prisoner’s Dilemma[5] as a dating show. The Bachelorettes wouldn’t be allowed to speak to each other before or during the game (duh). I think that they’d be able to hear each other’s responses, but I’m not sure. I/Dream-Show-Producer didn’t give that part much thought/go into detail, and I can think of reasons for allowing it either way. So, you’d have them either trying to throw the game by answering all the questions Incredibly Wrong [“If you were a flavor of ice cream, what would you be?” “I’d be vanilla, cause that was Hitler’s favorite flavor, and I really hate the Jews!”] which would provide comedy, or perhaps you’d have one person who’d end up trying to backstab the other bachelorettes out of a desire for companionship/greed for the trip, and try to give the Right Answers, Without Coming Off As Merely Trying To Give The Right Answers But Actually A Very Good And Decent Human Being. If the responses were open, you might get a bit of infighting, which seems to resonate with the kids of today. And you’d get people trying to change strategies halfway through. If the responses were closed, you’d get to see the various dynamics of the Prisoner’s Dilemma In Action, where you might have, say, Hitler-Answer, Manipulative-Answer, Hitler-Answer, or all three Hitlers, or all three Manipulative, or whatever.

I think that the closed responses would probably be best suited for a geek gedankenexperiment rather than an actual game show, although open answers would lessen the Prisoner’s Dilemma-ness of the whole thing, since the whole thrust of it is whether or not to lie based on not knowing what the other person will do. The problem then would be, after a while, it’d seem that the bachelorettes would be more tempted to just only give Hitler Answers (aside from the aforementioned occasional backstabber).

I think I would actually prefer closed answers, honestly, just because the game would be a little more interesting. Especially since the Bachelor has no real incentive either way[6], it’d be hilarious to see the contrast between the people who think everyone’s going to give Hitler Answers and the one-or-more who are trying to sell out the others. The “switching strategies” thing might be cool initially, but I have a feeling it’d get a little old, because you’d figure it’d probably happen every time where, one and two give Hitler answers, three gives a Manipulative Answer, and One and Two go “Hey, no!” and start giving Also Manipulative Answers, and I have a feeling the Manipulative Answers wouldn’t be nearly as funny/interesting/entertaining as Hitler answers, since I’d wager there’s way more answers that you can give that you’d expect to be “wrong”, but only a few that you’d expect to be “right”.

I don’t know, it seemed a rather interesting twist in the dream. And it still does. At least, way more interesting than the real Dating Game was. Which, well, even though I like Chuck Barris‘ ideas, The Dating Game was pretty dull, because it was basically “What flavor of ice cream etc?” “I’d be sex flavor, because I like to have sex!”. Which sort of comes pre-boring-after-a-while. It’s boring-after-a-while out of the box.

[1] I’m just going to use a setup of Bachelor/3 Bachelorettes, since that’s how it was in the dream-explanation, and it’s also easier, and I don’t have to do he/she all the damn time and keep explaining that sort of thing.

[2] Again, adjust for gender, as mentioned in FN1. Just so you don’t think that the male contestant(s) always get the trip, because that would just be stupid. It wouldn’t even work when I get to the later bits of the explanation.

[3] Or, if the bachelor was a lady, her brother. Or if the show were progressive enough to actually have gay couples on (whoa, real life gay people on TV?), they’d take their sibling of the appropriate gender. The joke of this part of the game was a bit of implied incest, even though it wasn’t ACTUALLY expected that, y’know, they would have, uh, relations. It was just that sort of implied naughtiness that the original had, just with the added comedy of, y’know, “sisters and brothers make better lovers”, in the words of E. I have no idea what would happen if the contestant didn’t have an appropriate sibling. I assume they’d either not let, say, an only-child on, or maybe go for first cousins. The implied incest is the important thing.

[4] So, if you want to get technical, the options are:

'Lor    'Lette1   'Lette2   'Lette3
20k       5k        5k        5k  
20k      20k       RaR       RaR  
20k      RaR       20k       RaR  
20k      RaR       RaR       20k

[5] Kinda-sorta, anyway. (Feel free to skip this footnote if you’re familiar with PD.) In the original one, it’s two prisoners in a jail (uh, there’s lots of different versions, this is the one I’m probably most familiar with. The same principles apply anyway.), and they’re awaiting trial. The lawyer presents each with a deal: If they both confess, they each spend 4 years in prison. If one confesses, but the other doesn’t, the confessor goes free, but the other spends 5 years in prison, but if neither confesses, they both spend 2 years in prison; (I guess the Man has info on smaller stuff, but they want to go for the big crime if they can, if you demand a real-type explanation for these crazy rules.). But they’re in separate rooms, so they don’t know what the other’s doing. So, the table looks like:

                 Confess        Doesn’t 
 B  Confess    [A=4, B=4]     [A=5, B=0]
 b  Doesn’t    [A=0, B=5]     [A=2, B=2]

So, in the real one, it’s individually better for you if you actually confess, because there’s the greatest reward (so, if you’re Alex, you want to confess, since that means you COULD go totally free, and spending time in prison is not something you’re really into) BUT if you don’t confess, you’re either in prison for the long haul, OR if you both don’t, you both get pretty good results (but not optimal). So, you’re trying to successfully backstab the other without getting horrible prison time. So, the question is; do you try to be the backstabber and hope the other guy’s honest-by-being-dishonest, or do you be honest-by-not-being-honest and hope that Bob doesn’t make you into a sucker.

This isn’t QUITE the same thing; it’s similar though. In this one, there’s a wild card (the Bachelor; we assume that he doesn’t care, and will choose what’s best for him; although he could be a Well-Meaning Sort and wouldn’t choose anyone even if the future love of his life was behind the door, so she (and two other women he doesn’t know) could get five grand, or he could be a bitter sort (maybe one of the Bachelorettes has gone too far) and doesn’t care what he does so as long as she loses. Or he could just be a nut and not actually choose “correctly”; i.e. if presented with Good Answer, Good Answer, Hitler Answer, go for the Hitler Answer on a lark. So, uh, yeah. It’s a bit of a wrench in the works that sort of has the possibility to make everything for naught.). Also, it’s based more on reward rather than penalty, which shouldn’t matter from a mathematical standpoint, which could do weird things to the way the game is played strategically (but this is a little harder to justify the explanation of change. While 5 grand isn’t nothing to sneeze at, it’s not guaranteed (you don’t know if someone’s going to attempt to sell you out), and 20 grand’s a lot better than 5. And, as mentioned in the wild-card bit, just because someone’s attempting to sell the others out doesn’t mean it will actually work (since in the real one, it’s just a simple two state thing, no interpretation of a judge or anything required. I suppose if you want, you could throw in an extra column of the Judge and/or Jury, and to whether or not they’d been hitting the hooch before the trial, or whatever other explanation you want to think of.)

Digressions aside, my point is, this isn’t a true Prisoner’s Dilemma Problem, but it’s close enough for horseshoes and hand grenades. Also: Feel free to check my explanations/arguments/whatever — I’m not the best at math-type-stuff, and it’s been years since I did much reading on this. This probably isn’t that right or rigorous as you’d get from other people, but it should at least get the gist across pretty well, and I don’t think I missed any Big Bad Points of the PD, anyway. (Well, aside in not getting into strategies of it, i.e. Tit-For-Tat (in repeated games, always not confessing until someone sells you out, at which point, you just start copying their play from the previous round. So, if they confess, next time you confess. If on that time, they don’t confess, you don’t; if they confess again, you confess again.), which is pretty much accepted as the best policy, at least if you’re a computer, anyway. There were a few trials with different rule sets, and it seemed that Tit-For-Tat tended to come out on top.)

[6] I’d assume he’d have to, at least sort of, pick the relative; i.e., if his sister was on very, very poor terms with him, he’d have an incentive to go with someone, anyone, other than her. So, he’d probably pick the best person for him, be it sister or contestant. Or perhaps not, for reasons outlined in FN5 above.


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