The ganch gamble
[Translated from Yu. V. Pukhnatchov, Yu. P. Popov. *Mathematics without formulae*. - Moscow. - ‘Stoletie’. − 1995. - pp. 404-405. All mistakes are my own.]
The East is famous for her legends… They say that once upon a time, in a certain town, there lived two well-known carvers of ganch (alabaster that hasn’t quite set yet.) And their mastery was so great, and their ornaments were so delightful, that the people simply could not decide, which one is more skillful.
And so a contest was devised. A room of a house just built, which was to be decorated with carvings, was partitioned into two halves by a [nontransparent] curtain. The masters went in, each into his own place, and set to work.
And when they finished and the curtain was removed, the spectators’ awe knew no bounds...
… for the ornaments in both halves were identical, up to the smallest cartouche!
Only when the people looked closely at their work, they saw that one master did his part conscientiously, and the other decided to apply his wit, and polished the walls into mirrors, so that they reflected the embellishments on the other walls.
The legend says that the victory was given to the second one. And we, as mathematicians, would without doubt join this decision. For having turned the walls into mirrors, he exhibited not only mastery (of which everybody already knew), but also a deep understanding of the very nature of ornament, which lies exactly in the repetitiveness of the elements. […]
So! The first one cooperated, the second one defected:) and if both defected or both cooperated, the room would be worse off, though at least in the last case the carvers would still be judged for their skill… No associations, anyone?:))
The mirrored side breaks the rooms usage as a tiled room. If you walk in you will see your reflection and see less of the pattern than if the details were actually copied. Design that doesn’t survive use. The “wit” is more smartass than wise.
One could also argue that by the same logic having both halfs as mirrors would have been a superior room as it would have been way more repetetive. That highlights that it is more concept art than esthetics.
It’s worse than that; it doesn’t work at all. To give the impression of an exact copy of the other side’s ornamentation you’d need a mirror across the middle of the room. But I take it the literal meaning of the story is not really the point and it’s not very important that it wouldn’t work in real life.
I don’t think cooperate/defect are good action labels because it doesn’t seem much like a standard prisoner’s dilemma. It is not quite a game of Chicken either, but it is closer to Chicken than PD.
The mirror/mirror outcome in Ganch is like getting in a car crash in Chicken, because it is the worst for everyone and anyone who swerves unilaterally will make both happier with the outcome, and that outcome potentially functions as a threat to use against the other player to get your way if a conflict comes up.
Ganch is unlike Chicken in that Chicken’s swerve/swerve outcome gives an honorable tie, and the other person playing a different move causes you to lose outright, which is something you’d like to prevent if you can.
Contrast this with the carve/carve outcome in Ganch, which is worse than having the carving role in a carve/mirror outcome, because playing carve against mirror at least the room looks OK but playing carve against carve leaves you with an artistic mess and both of you look bad. So in Ganch (unlike Chicken) the players have the same worst and second worst outcomes and these outcomes are in a diagonal relationship to each other.
Basically, Ganch is a kind of coordination game and the closest “famously named” coordination game I know to Ganch is the 2x2 Battle Of The Sexes.
This name goes back at least as far as Duncan and Raiffa’s 1957 book “Games and Decisions: Introduction and Critical Survey”, reviewed here.
The basic dynamic in BotS is that you are playing a coordination game, but not a coordination game with perfect alignment of goals. It is generally silly to play coordination games without talking first, but in this variant the conversations are more delicate than otherwise because there’s some of self-interest and meta-game-fairness issues that come up when picking which of the two “basically acceptable” Nash equilibriums to aim for.
And yet carve/carve is what they were expected to do and be judged for...
They set up the problem really badly, then. What they asked for would not have looked good at all.
Perhaps the loser had to redo his part after the winner’s. Oh wait...:)
Arguing for or against a parable is going to lead nowhere ever.
Having said that; cute story. I think the value of this story is that not all problems should be solved in a straightforward way; not in the Cooperate or defect or win/lose result of the story.
What if they kicked the mirror-maker out of town and awarded the actual worker? Not so fabulous now huh...
“What if they kicked the mirror-maker out of town and awarded the actual worker?”
This is the question I keep asking myself. In the story as written, the village rewards the clever skilled worker over the diligent skilled worker. This might work in the short term, and the clever worker’s gamble pays off for him personally as he sees increased business from increased prestige. If we consider the village (or the judges) to be actors in the game, however, they act in their own disinterest by disincentivizing craftsmanship in favor of craftiness. And here I am, arguing for or against a parable...
emphasising again—cute story.
The advantage of creative writing is you get to write all the characters. and all the scenarios and re-write so that this character wins and that character loses. While we like to think we discovered the cleverness as the villagers did; in reality the story was created to boast the writers ability to demonstrate this piece of cleverness. not really as a reflection on the real world...
I searched dictionaries up and down and could not find “ganch”. Closest thing I found is that this is an Uzbek word which gets transliterated to English as ganch or ganj. http://withasiainlove.blogspot.com/2014/05/ganch-art-of-central-asia.html
Deleted because others found the same.
Consider what the payoff matrix is in this case, and what strategy maximizes one’s payoff.
I am not sure, I think defecting maximizes one’s payoff the first time, but if both defect, the second time it is better to cooperate, since another polished room would only make the judges laugh.
“Ganch” was an unknown word for me, so I googled it and found out that...
Ouch.
“Ganch” was an unknown word for me too, so i googled it and the first link was from Urban Dictionary… I’ll not say what I found, it is inappropriate.
But then I searched some more, quite a lot, until I found this definition, from the Great Soviet Encyclopedia:
Ganch: Middle Asian name for a binding material obtained by heating rock containing gypsum (from 40 to 70 percent) and clay. An aqueous solution of pulverized ganch sets quickly (hardens) and is easy to mold. From the first centuries of the Common Era ganch was used as a material for plaster, volumetrical and plastic decor (carving, casting of lattices and other parts), and sculpture. Wet ganch can be cut easily and allows both bas-relief and high relief to be diverse and have fine details. Carved ganch has a pleasing white mat surface. A layer of slightly wet ganch serves as a base for wall paintings. In the Caucasus it is called gazha.
Yes, it’s basically a variety of gypsum plaster. This may be helpful as the context for the OP...