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.
1 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.
Schelling Point Strategy Training
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:
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.
1 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.