Solve for the equilibrium

by on August 25, 2012 at 4:24 pm in Current Affairs, Games | Permalink

Here is the short video.  Here is text with photos and another video.  Five Ukrainian women, in an Ukrainian art museum.  They are sleeping, or rather pretending to sleep, dressed up as Sleeping Beauty.  Men come along and kiss them, on the lips, with each man allowed only one kiss.  They have all signed legally binding contracts.  If a woman responds to a kiss by opening her eyes and “waking,” she must marry the man.  The man must marry the woman.

Who will kiss?  When do eyes get opened?

The museum gives out free breath mints.

For the pointer I thank the excellent Daniel Lippman.

1 dirk August 25, 2012 at 5:32 pm

Solution: dorks kiss, nobody’s eyes open.

2 Peter August 25, 2012 at 5:32 pm


3 The Other Jim August 25, 2012 at 9:29 pm

i beg to differ.

Given that the entire purpose of “art” is to attract attention, and someone like you is paying enough attention to it to take time out of your day and comment on it, this is a pretty freaking brilliant idea.

4 SPH August 25, 2012 at 5:41 pm

The woman has a monopoly on her hand to marriage, with full discretion. There is also serious information asymmetry, given that her eyes are closed. Assuming the woman is rational, the equilibrium is she stays “asleep”.

There are a ton of confounding factors, like the woman’s commitment to some ideal of “high art,” or perhaps something about her means she will never meet & marry a respectable suitor the traditional way (hopefully not halitosis) — either way, as the prospective groom I would have my fingers crossed that she stays down

5 Patrick Warren August 25, 2012 at 6:06 pm

Serious self-selection bias. The men most likely to sign the contract are those that think their chances of finding a spouse are low, for whatever reason–likely undesirability. Men who think themselves marketable are unlikely to risk binding themselves to an unknown. Equilibrium says sleep.

6 Miley Cyrax August 25, 2012 at 6:41 pm

‘One of the women, Natalia, said “It seems to me that if it’s my boyfriend, I will feel it on an intuitive level. Secondly, if I don’t feel it, I won’t open my eyes. Anything can happen in life. And suddenly its fate? What if it’s the only way I’ll meet my soul mate?”‘


The girls are self-selected for naivete and general stupidity, and selected for looks by the organizers (I jumped around in the video, I saw two girls and they both seemed decent). The men are self-selected for desperation, the kind of men who would roll the dice on random decent-looking women who would normally be out of their league.

7 Affe August 25, 2012 at 6:44 pm

Do you have to kiss them, or can you just romantically lick their face while grunting and snuffling ?

8 SPH August 25, 2012 at 6:59 pm

Good point. Maybe the trick for an “awakening kiss” is brute force.

9 Some random commenter August 25, 2012 at 8:24 pm

Perhaps I am an uninformed commenter but I wonder whether you pronounce the u in Ukrainian the same as the u in uniform or the u in underwhelming?

10 wonderball August 25, 2012 at 8:52 pm

Well done, sir.

11 Tyler Cowen August 25, 2012 at 9:29 pm

I don’t think any of you have solved for the equilibrium, not yet.

12 sph August 26, 2012 at 12:04 am

Is it, short run she stays asleep, long run one fool wakes up, the marriage is confirmed, and the exhibit retires a ‘success’?

13 Ajit August 25, 2012 at 9:59 pm

First she could make up here mind for :
1) An estimation of number of people going to kiss her. (n here)
2) She will be judging solely based on the kiss .. as no other alternative.
Then may be it could be related to Marriage problem 🙂 Then may be reject n/e prospective ones and then choosing the one who is better than all past kissers 😛

14 Insecure Sinecure August 25, 2012 at 10:14 pm

This is how I met my wife. 22 years.

15 Jim August 26, 2012 at 7:11 am

Yep. That’s how how I met your wife too. 🙂

16 bluto August 25, 2012 at 10:29 pm

I’d use a prearranged signal, and would expect the boyfriends are the ones being played, as the girls are forcing a commitment decision (not kissing or not delivering the prearranged signal and they lose face, kissing and they’re committed to a wedding).

17 Millian August 26, 2012 at 3:30 am

But they don’t lose face.

18 Tyler Cowen August 26, 2012 at 7:15 am

Now you are getting somewhere…

19 Slocum August 26, 2012 at 7:37 am

I think there are ‘multiple equilibriums’ here:

– Girl with boyfriend, boyfriend participates, prearranged signal (bluto’s scenario).
– Girl with boyfriend, boyfriend doesn’t participate, girl wants boyfriend to be jealous and worry about losing her — hoping for a commitment that way. Girl stays asleep.
– Girl with no boyfriend who wakes randomly in order to become an instant celebrity. Divorces ‘storybook prince’ shortly after publicity dies down.
– Evil prince boyfriend who’s growing tired of girlfriend and doesn’t like having his hand forced. He agrees to prearranged signal and then provides it to a random doofus in line.

20 Claudia August 26, 2012 at 9:15 am

Slocum, so where’s the ‘true love’ equilibrium? Bluto’s signaling outcome sounds a bit too engineered to me to count. This whole thing is a bit extreme (err artistic), but relationships usually start with some random connection. The saying is love at first sight, not at first kiss, but what’s the difference really? One of these women will ‘wake up’ …what a great story and she’ll have found a guy who believes in fairy tales too (to each their own). And several of the women won’t wake up and will have a great line for later relationships…finally found her prince. Not sure how the rejected suitors will use it (hopefully they won’t), Relationships are dynamic games not static equilibria, but this is a pretty fun one to consider. Now it either ends with the American version of ‘they lived happily ever after’ or the German version ‘if they’re not dead yet, they’re still alive.’

21 Nikaps August 25, 2012 at 10:40 pm

Of course this is going to be a reality TV show. There is a secret code word that the right boy says, she opens her eyes and they live happily ever after in the glare of 24×7 cameras. Well, until the big breakup and bigger re-unification and…:)

22 Tony August 25, 2012 at 11:03 pm

If I were the woman, the problem would be straightforward in principle, since the optimal solution would be to marry the man with the largest mustache.

Assuming mustache size were Pareto distributed, and kisses arrived as a Poisson process, I would run some simulations of different strategies and adopt the one with the greatest expectation value for mustache size. At a guess, after undertaking such a study, I would end up doing something like this: Wait out the first half of the game while gathering data on mustache distribution. In the second half of the game, keep an eye on the expected number of kissers remaining, and wake up for whoever had a mustache larger than what I’d expect among the remaining kissers.

You can assume that I would be able to evaluate the size of a mustache while being kissed with my eyes closed. (Believe me, I have lots of practice, gender notwithstanding. And I’m not really kidding about the scoring function, either.)

23 Brian Donohue August 26, 2012 at 12:31 am


24 John August 25, 2012 at 11:25 pm

As has been pointed out given the lack of information only men with few options are likely to kiss. Therefore, no eyes open. Therefore, no kissing since even men with low value will know that eyes will not open. So the equilibrium is that no kisses happen and the mints stay untouched.

25 John August 25, 2012 at 11:26 pm

or more realistically only men who want to cop a feel use the mints.

26 Rahul August 26, 2012 at 12:54 am

They have all signed legally binding contracts.

Can such a contract be legally enforceable? I doubt it, at least in Western nation law.

27 Go Horns! August 26, 2012 at 6:15 pm

You won’t get performance but you will get damages.

28 Ryan Langrill August 26, 2012 at 1:57 am

I think the key is that each man only gets one kiss… Presumably the women will know their relative attractiveness to the other women. Low status men will choose the ‘less attractive’ women, hoping that they will open their eyes, since their options are not as good. This means that high status men will choose the attractive women, which means the women have the incentive to open their eyes. At least, for the men who kiss assertively, since it indicates a high self-esteem/experience (which in turn indicates a sort of quality). Timid kisses might indicate high risk preference/low-status men. (and the lowest self-esteemed men won’t be in public/won’t go to kiss). The ‘least attractive’ women will not open their eyes. The second most attractive woman is the second most likely to open her eyes, and so on. Breath mints decrease the willingness of women to open their eyes, since it signals less casual hygiene and/or more desperation.

Of course, this ignores any possible selection effects. If a similar level of enjoyment of modern art is a margin along which marriages succeed, more women will open their eyes.

This also ignores expectations, and expectations of expectations…

29 Rob August 26, 2012 at 3:41 am

That’s a nice model. I worry though that it would be undermined by unattractive men pretending to be attractive men and taking a chance by kissing the most attractive women. If the men are ‘risk loving’ regarding the attractiveness of their partners, while the women ‘risk averse’, the equilibrium will remain ‘eyes closed’.

You could add in to the model that the men don’t have much to gain by marrying someone much more attractive than them, because if they aren’t desirable enough sustain the relationship, their partners will ultimately leave anyway.

30 Non Papa August 26, 2012 at 12:36 pm

Agreed. The low-status men understand that an “assertive kiss” signals confidence/desirability. This is easy to fake, especially because the payoff — hypergamy — is very large.

31 economist1 August 26, 2012 at 2:02 am

This seems to be an interesting variety of the Secretary Problem:

Not sure if this is the same solution- it is a nice reversal of the origin gender roles, though with eyes closed this time. The sample size seems to be too small to really solve for the solution in practice.

This description of the problem from wikipedia is more relevant for marriage than a job, though I guess divorce is always possible: “Immediately after an interview, the interviewed applicant is either accepted or rejected, and the decision is irrevocable.”

32 Hei Lun Chan August 26, 2012 at 9:22 am

Isn’t it difficult for a normal human being to close her eyes for a long time without falling asleep or being very uncomfortable? How long do these women have to keep their eyes shut? Hours at a time? What if one of them opens her eyes accidentally?

33 Non Papa August 26, 2012 at 12:39 pm

If the article is correct, the woman’s contract says “If I open my eyes while being kissed, I agree to marry the kisser.” The operative part being “while being kissed.” As long as she is not being kissed (presumably, if her eyes are open, she can avoid being kissed), she can have her eyes open. In reality, I imagine the exhibit organizers let the women open their eyes/get up/walk around every so often, during which they keep prospective suitors out.

34 No Princes Here August 26, 2012 at 3:09 pm

I would have expected the equilibrium to be that it’s in none of the women’s interests to open their eyes for random suitor, so every suitor safely grabs a kiss from a beautiful woman confident that he won’t have to marry her.

35 Surely they're not all frogs August 26, 2012 at 5:38 pm

Why are the women there then? To get smooched by a bunch of guys who need breath mints? Doesn’t sound like a stable equilibrium to me.

36 Adam August 26, 2012 at 4:22 pm

I’d think “equilibrium” here would heavily depend on Ukrainian divorce laws. If you can get divorced the next day for the cost of a court fee, there isn’t a huge disincentive to at least give it a shot. Plus, if it’s really just eyes opening, the two parties can still talk to each other for as long as the museum is open each day and the woman can feel the man to get an idea of his physical prowess. I’m not even convinced the ability to open your eyes matters much at that point.

37 Jdetal September 8, 2012 at 2:25 pm

The women can keep their eyes closed and obtain a signal, i.e. Selection, at no cost. Selection can be pursued later at the woman’s option.

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