# Schelling Point Strategy Training

8 04 October 2013 03:41PM

There's a category of game-theoretic scenario called Battle of the Sexes, which is commonly used to demonstrate coordination problems. Two cinema-goers, traditionally a husband and wife, have agreed to go to the cinema, but haven't decided on what to see beforehand. Of the two films that are showing, she would rather see King Kong Lives, while he would rather see Big Momma's House 2. Each would rather see their non-preferred film with their spouse than see their preferred film on their own. The payoff matrix is as follows:

 Husband King Kong Lives Big Momma's House 2 Wife King Kong Lives 2 / 1 0 / 0 Big Momma's House 2 0 / 0 1 / 2

The two have not conferred beforehand, beyond sharing knowledge of their preferences. They are turning up to the cinema and picking an auditorium in the hope that their spouse is in there.  Which should they pick?  This is a classic coordination problem. The symmetry of their preferences means there is no stand-out option for them to converge on. There is no Schelling Point.1

Except I'm going to argue that there is.

Shoehorning an example of a Schelling Point into the above scenario, we might imagine that one of the above films being screened is being billed as "an ideal romantic treat to share with your spouse", (which one that would be, I'm not entirely sure), though in the absence of a "natural" Schelling Point, there's no reason we can't make one. All we need is to identify procedures that would reliably elevate one of these options to our attention.  Then it becomes a question of selecting which of these procedures is most likely to be selected by the other agent in the scenario.

I am now going to instigate a multidimensional instance of Battle of the Sexes with all the readers of this post.  Below are sixteen randomly-ordered films.  I am going to select one, and invite you to do the same.  The object of the exercise is for all of us to pick the same one.  I will identify my selection, and the logic behind it, in rot13 after the list.

Breakfast at Tiffany's
William Shakespeare's Romeo and Juliet
E.T. the Extra-Terrestrial
Children of the Corn
An American Werewolf in London
To Kill a Mockingbird
Harold and Maude
The Day the Earth Stood Still
Duck Soup
Highlander
Fantasia
Heathers
Forbidden Planet
Butch Cassidy and the Sundance Kid
Grosse Pointe Blank
Mrs. Doubtfire

Urer vf na vapbafrdhragvny fragrapr gb guebj bss crbcyr jub pna vagrecerg guvf plcure ba fvtug ol abj. Zl fryrpgvba jnf na nzrevpna jrerjbys va Ybaqba. Gur cebprqher V fryrpgrq jnf gur svefg svyz nycunorgvpnyyl. Guvf frrzf yvxr gur zbfg "boivbhf" cebprqher sbe eryvnoyl fryrpgvat n fvatyr vgrz sebz gur frg. Cbffvoyl n zber "boivbhf" bar jbhyq fvzcyl or gb fryrpg gur svefg bar ba gur yvfg (Oernxsnfg ng Gvssnal'f va guvf pnfr), ohg V jnf bcrengvat ba gur nffhzcgvba gung gur yvfg jnf abg arprffnevyl eryvnoyl-beqrerq (juvpu V gevrq gb pbairl ol qrfpevovat gur yvfg nf "enaqbzyl-beqrerq", ohg pbhyqa'g ernyyl rkcyvpvgyl fgngr jvgubhg cbffvoyl tvivat n ovt uvag nf gb gur cebprqher V pubfr. Guvf jbhyq unir fcbvyrq guvatf n yvggyr.

I have no idea if that worked.  Whether or not it did, it seems to me that the general skill of identifying popular procedures for designating Schelling Points is possibly a worthwhile skill to develop. It also seems to me that once a handful of common strategies for identifying Schelling Points are known to a group, some effort has to be put into constructing scenarios in which that group can't coordinate. This forms the outline of an adversarial game, (provisionally named Schelling Point Strategy Training), whereby two teams take it in turns to construct and present a set of options which the other team has to coordinate on. I am idly toying with running a session of this at a future London Less Wrong meetup.

There is actually an unrelated meta-strategy here, whereby on all disputes one designated partner acquiesces to the wishes of the other.  This behaviour is also far from unheard of in romantic partnerships.  While this doesn't seem very egalitarian, I am wondering if it actually becomes a reasonable trade-off for partnerships which face coordination problems on a regular basis.

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Comment author: 04 October 2013 03:49:24PM *  10 points [-]

Below are sixteen randomly-ordered films. sixes_and_sevens has selected one, and invites you to do the same. The object of the exercise is for all of us to pick the same one

Comment author: 05 October 2013 08:09:34PM 4 points [-]

I think the intended Schelling point on the list would have been much more reliable if you had emphasized that we were to imagine that the presentation order was different for each of us.

I'm pretty sure that I would have gotten it if that had been stated (of course, someone might not notice).

Comment author: 05 October 2013 08:27:22PM 1 point [-]

Well, yes, but as addressed in the rot13 block, I couldn't emphasise that without offering a substantial clue as to my procedure of choice.

I could perhaps have phrased it as "you are handed a stack of DVDs with these titles: pick one".

Comment author: 06 October 2013 01:46:35AM 2 points [-]

I pick the uppermost one, of course.

Comment author: 06 October 2013 01:58:21AM 0 points [-]

I can't tell if this is sarcasm.

Comment author: 07 October 2013 03:01:23AM 1 point [-]

It's not, why wouldn't that have worked?

Comment author: 07 October 2013 09:12:57AM 1 point [-]

Because the order of a stack of DVDs is considerably more fragile than the order of a static list of items on a webpage. The next person to receive the stack of DVDs and make the decision will not necessarily receive them in the same order. That was the whole point of describing the choice as selecting from a stack of DVDs.

Comment author: 14 November 2013 03:29:51AM *  3 points [-]

(Late to the party, but what the heck.) Rather than a stack, a good trick to avoid the tip-off might have been to describe the set of movies as "a scattered mess of DVDs in a box; in no particular order, they are..."

Comment author: 14 November 2013 10:19:21AM 2 points [-]

I will probably adopt something like this in future iterations of this exercise.

Comment author: 06 October 2013 04:01:59AM 1 point [-]

You said that, but I don't accept it. All that does is tell us not to use the SUPER-obvious Schelling point of 'the first one'.

Comment author: 06 October 2013 12:47:33PM *  2 points [-]

This might be hindsight bias, but I'm pretty sure that if I were approaching this problem from the outside, and the author said "by the way, don't use the order in which it's presented here", this would immediately draw my attention to the general idea of ordering procedures.

Comment author: 07 October 2013 03:16:34PM 2 points [-]

The idea of finding an ordering procedure is also raised by saying that we're seeking a Schelling point.

Comment author: 04 October 2013 05:03:41PM 3 points [-]

There is actually an unrelated meta-strategy here, whereby on all disputes one designated partner acquiesces to the wishes of the other. This behaviour is also far from unheard of in romantic partnerships. While this doesn't seem very egalitarian, I am wondering if it actually becomes a reasonable trade-off for partnerships which face coordination problems on a regular basis.

How common Battle of the Sexes situations are in real life? Almost always the partners can talk to each other, making strategies like ‘let's flip a coin’ or ‘I decided the last time, so you decide this time’ viable. (Also, if you face coordination problems that often, you probably aren't the right partner for each other and had better break up.)

Comment author: 04 October 2013 05:47:30PM 5 points [-]
Comment author: 05 October 2013 04:31:01AM 2 points [-]

Also, many nonrationalists have naive ideas about how being in a Romance means you automagically never have coordination problems.

Comment author: 04 October 2013 08:23:45PM 0 points [-]

It doesn't sound like the “meta-strategy here, whereby on all disputes one designated partner acquiesces to the wishes of the other” could apply to those.

Comment author: 04 October 2013 10:28:17PM 4 points [-]

When my old roommates and couldn't find each other at CostCo, we coordinated by having the short people look for the tall people and the tall people not move around too much.

In games like The Resistance, hidden players sometimes need to coordinate. My friend circle has a convention where the more experienced player chooses.

Comment author: 04 October 2013 06:47:58PM -1 points [-]

How common Battle of the Sexes situations are in real life?

Seriously? Extremely. Conscious or subconscious manipulation is pervasive. Implicit or explicit threat of withholding sex or a promise of granting sex ("I'm not in the mood after a movie like that" or "someone is getting lucky tonight!") is not even considered manipulative anymore.

Comment author: 05 October 2013 11:03:55AM 3 points [-]

In this case you have a bargaining problem, not a coordination problem.

Comment author: 05 October 2013 08:03:15PM 0 points [-]

Even so, that's not what the quoted question was asking.

Comment author: 06 October 2013 12:11:40AM 1 point [-]

The question was about games where communication is not allowed. If you have bargaining then you have communication.

Comment author: 05 October 2013 01:52:44PM 0 points [-]

The two aren't mutually exclusive.

Comment author: 05 October 2013 03:57:24PM 2 points [-]

Yes, but if communication is possible, the issue of mutually guessing which Nash equilibrium the other player is going pick doesn't occur.

Comment author: 05 October 2013 04:28:52AM 1 point [-]

I don't see "I'm not in the mood after a movie like that" as manipulative. There are movies that, while I may enjoy watching them, will leave me in a melancholy mood that just isn't consistent with being horny. Though yuck at "someone is getting lucky tonight!"

Comment author: 19 October 2013 08:02:20PM 0 points [-]

a melancholy mood that just isn't consistent with being horny

That's what foreplay is for. ;-)

Comment author: 04 October 2013 07:34:06PM 1 point [-]

is not even considered manipulative anymore

Depends on the relationship, I'd say, on the "cultural norms" established within it. In some it's fine, in some it's fine only if open and explicit, in some it's not fine at all.

Comment author: 04 October 2013 08:43:33PM -2 points [-]

So, one partner decides which movie to watch and the other decides whether to have sex. That's the second of the strategies I mentioned in the grandparent. :rolleyes:

Comment author: 04 October 2013 09:15:40PM 3 points [-]

It's rarely like that. It's more like "it's my way in all things I care about, or you are not getting any".

Comment author: 04 October 2013 11:09:32PM 1 point [-]

In which case the two clearly ought to break up.

Comment author: 04 October 2013 11:16:43PM 6 points [-]

Not "clearly", unless at least one of them would be unambiguously better after the break-up than after any other possible course of action, like counseling, cheating, confronting, bluffing, learning how to influence people, etc.

Comment author: 06 October 2013 08:22:32PM 0 points [-]

I mean, if A is willing to refrain from sex with B arbitrarily long in order to get their way but not vice versa, then A probably doesn't really want sex with B that much; so it's likely that A would be better off with someone else with less sex drive than B, and B would be better off with someone else with more sex drive than A. (Unless they're both fine with the idea of trading sex for favours, in which case yeah, whatever works.)

Comment author: 07 October 2013 03:54:50AM 1 point [-]

These are certainly some of the possible alternatives, but not all of them.

Comment author: 04 October 2013 04:01:57PM 3 points [-]

66&77, I picked your selection for the same reason you did.

Comment author: 04 October 2013 04:08:09PM 2 points [-]

It's good to know I'm not completely imagining this as a reasonable strategy.

Comment author: 04 October 2013 04:55:33PM 2 points [-]

Ybgf bs crbcyr erfcbaqrq gb yvfg beqrevat, be svyz zrgnqngn. V jnf cerggl qvssrerag va gung V gevrq gb pubbfr Gur Yrff-Jebatvrfg Svyz. Naq snvyrq, gubhtu V jnfa'g nybar.

Comment author: 04 October 2013 06:33:04PM 0 points [-]

Which film was that?

Comment author: 05 October 2013 04:29:35AM 0 points [-]

I can't remember... I think TKAM?

Comment author: 04 October 2013 04:36:52PM 2 points [-]

What will the most common answer to this question be?

What will the least common answer to this question be?

Comment author: 04 October 2013 11:42:35PM 2 points [-]

I got 'em both right! Yeah!

Comment author: 05 October 2013 04:41:16AM 1 point [-]

Me too! I must admit I am feeling quite pleased about getting the second one. I missed the movie question though.

Comment author: 05 October 2013 06:39:26PM 2 points [-]

I was frustrated that I didn't manage to get both right, but then I realized that the only reason my choice on the second wasn't the winning answer was because of my own vote. There's no winning answer! No fair!

Comment author: 04 October 2013 06:32:11PM 2 points [-]

For the second question I randomised and ended up with the most popular answer. :-(

Comment author: 11 October 2013 05:23:41AM 0 points [-]

Got them both right.

The first one's pretty obvious. Reasoning for the second one: gjb guebhtu sbhe ner gur boivbhf nagv-Fpuryyvat pubvprf, fb anvir nafjref jvyy yvxryl or fcyvg orgjrra gurz. Rira ba n fvgr yvxr guvf bar, gurer jvyy cebonoyl or rabhtu anvir nafjref gb rkpyhqr gurz nf pbeerpg erfcbafrf. Bar vf gur zbfg fnyvrag nafjre bapr lbh fgneg guvaxvat nobhg nibvqvat pbbeqvangvba cbvagf, fb jr'yy cebonoyl frr gung bar n ybg gbb. Svir vf gur bgure boivbhf pbbeqvangvba cbvag, ohg gur yrff boivbhf bs gur gjb, fb vg'yy zbfg yvxryl frr gur srjrfg cvpxf birenyy.

Comment author: 05 October 2013 08:06:35PM 0 points [-]

Nailed question 1, obviously. Second question, I was the 9th vote or it and the least popular had 7 votes (most popular are tied at 13)

Comment author: 05 October 2013 04:58:27PM 0 points [-]

V qrpvqrq gung gur orfg jnl gb nibvq ybfvat ba gur frpbaq dhrfgvba vf abg gb cynl. Npghnyyl abg ibgvat ba gung dhrfgvba vf gur yrnfg pubfra bcgvba.

Comment author: 05 October 2013 03:45:50PM *  0 points [-]

I got the first one right, but apparently there are 2 right answers to the second question right now. And I didn't choose either of those.

Comment author: 04 October 2013 04:13:17PM 2 points [-]

I failed at coordinating with you (and any other who took the poll before me). Sbe zr n zber angheny Fpuryyvat cbvag jura gur dhrfgvba vf juvpu zbivr gb jngpu vf gur bar jvgu gur uvturfg VZQO engvat, engure guna gur svefg va yvfg be va nycunorg, juvpu ner hapbaarpgrq gb vagevafvp dhnyvgvrf bs gur zbivr. Onfrq ba gung V pubfr Gb Xvyy n Zbpxvatoveq.

Comment author: 04 October 2013 09:36:53PM 1 point [-]

V nyfb snvyrq ng cvpxvat gur fnzr bar nf nalobql ryfr. V jnf cvpxvat haqre gur cerivbhf cerzvfr bs "trarevp qngr avtug", naq fb gevrq gb cvpx gur zbfg "qngr avtug-l" zbivr, juvpu frrzrq yvxr Ebzrb naq Whyvrg, juvpu vf na npgvbal ebznapr. (Nygubhtu, crefbanyyl zl zbivr qngr avtugf graqf gbjneq zber fpv-sv, fhcreureb, Wbff Jurqba, rgp, ohg gung'f zber bhgyvre-l guna trarevp, V guvax.)

Comment author: 04 October 2013 09:42:28PM 1 point [-]

That choice does seem to be more popular than chance alone would suggest. I was wondering why, but this is a plausible explanation.

Comment author: 11 October 2013 04:41:17AM 0 points [-]

Harold and Maude. By far, the film worth seeing once, or once more, on the list :)

Comment author: 05 October 2013 05:18:02PM 0 points [-]

Being able to reliably select a schelling point surely improves coordination in (large) groups but it doesn't neccessarily maximize utilons. At least the given obvious strategies have the disadvantage of selecting unique solutions but arguably ones that may yield less overall satisfaction.

On the movie example the best strategy may significantly depend on the number of participants (and options). Being alone in the movie is dissattisfactory for most but less likely if you are a large group in which case it'd be likely to meet somebody in any movie. In that case the best strategy is obviously to choose the movie you like most.

For a medium size group a strategy that is least likely to dissatisfy anyone may be a good strategy. I chose E.T. on the movie question for that reason which seems to be not that bad a real life choice (I didn't assume a romantic but a general setting due to the fact the the whole audience was invited).

[A] meta-strategy [], whereby on all disputes one designated partner acquiesces to the wishes of the other.

I always assumed that the partner doing the decision would choose the option preferred by the other who already has the burden of being late. This of course assumes that love is true and mutual thus both may assume good faith on the other. This may in itself by romantic and unrealistic though.

Comment author: 05 October 2013 03:25:39PM 0 points [-]

Vagrerfgvat. V jnf guvaxvat va grezf bs fhowrpg znggre bs gur zbivr. V gevrq gb rfgvzngr obgu jung traer bs zbivr gur nirentr YrffJebat crefba jbhyq yvxr gb jngpu, naq, bar fgrc erzbirq, gb rfgvzngr jung traer bs zbir gur nirentr YrffJebat crefba jbhyq cerqvpg gung gur nirentr YrffJebat crefba jbhyq yvxr gb jngpu. V qrpvqrq gung fpvrapr svpgvba jnf gur zbfg yvxryl traer, naq bhg bs gur guerr fpvrapr svpgvba zbirf, V cvpxrq Gur Qnl gur Rnegu Fgbbq Fgvyy.

Ybbxf yvxr bayl gjb bgure crbcyr pnzr gb gur fnzr pbapyhfvba. Bu jryy.

Comment author: 05 October 2013 03:48:30PM 0 points [-]

I wanted to follow the same strategy, but I knew only 1 of the films...

Comment author: 04 October 2013 07:34:25PM 0 points [-]

There is actually an unrelated meta-strategy here, whereby on all disputes one designated partner acquiesces to the wishes of the other. This behaviour is also far from unheard of in romantic partnerships. While this doesn't seem very egalitarian, I am wondering if it actually becomes a reasonable trade-off for partnerships which face coordination problems on a regular basis.

"Partner A gives on on odd days, and Partner B gives in on even days" seems pretty reasonable. I suspect the more common version, though, is something like "Partner A yields on what music to listen to, Partner B yields on what to eat for dinner" and so on through a lot of fairly specific categories. Which might or might not slowly build resentment on some of these categories but still seems better than one partner always losing.

Comment author: 04 October 2013 04:23:48PM *  0 points [-]

I think the strategy is generally going to be choose n "yrnfg" ryrzrag onfrq ba gur zbfg boivbhf beqrevat. Jung'f na boivbhf beqrevat?

• Beqre cerfragrq
• Yrkvpbtencuvpny bs Ratyvfu gvgyr
• Nycunorgvpny va Ratyvfu gvgyr ("Oynphyn" nurnq bs "N Avtug gb Erzrzore")
• Nycunorgvpny / yrkvpbtencuvpny beqre bs gvgyr va angvir ynathntr
• Lrne eryrnfrq
• ZCNN svyz ahzore
• VZQO ahzore
• Ohqtrg (erirefrq)
• Erirahr (erirefrq)
• Ynfg anzr bs qverpgbe
• Uhaqerqf bs bguref

Fvapr gur pubvprf jrer cerfragrq va n fgngvp yvfg, V jrag jvgu gur beqre bs gung yvfg.