… the effort of both players might be very different …
Covered in the glowfic. Here is how it goes down in Dath Ilan:
The next stage involves a complicated dynamic-puzzle with two stations, that requires two players working simultaneously to solve. After it’s been solved, one player locks in a number on a 0-12 dial, the other player may press a button, and the puzzle station spits out jellychips thus divided.
The gotcha is, the 2-player puzzle-game isn’t always of equal difficulty for both players. Sometimes, one of them needs to work a lot harder than the other.
Now things start to heat up. There’s an obvious notion that if one player worked harder than the other, they should get more jellychips. But how much more? Can you quantify how hard the players are working, and split the jellychips in proportion to that? The game obviously seems to be pointing in the direction of quantifying how hard the players are working, relative to each other, but there’s no obvious way to do that.
Somebody proposes that each player say, on a scale of 0 to 12, how hard they felt like they worked, and then the jellychips should be divided in whatever ratio is nearest to that ratio.
The solution relies on people being honest. This is, perhaps, less of a looming unsolvable problem for dath ilani children than for adults in Golarion.
″...I don’t see how that game is any different than this one? Unless you mean there’s not the reputational element.”
They just ignore the effort difference and go for 50:50 splits. Fair over the long term, robust to deception and self-deception, low cognitive effort.
The Dath Ilani kids are wrong according to Shapley Values (confirmed as the Dath Ilan philosophy here). Let’s suppose that Aylick and Brogue are paired up on a box where Aylick had to put in three jellychips worth of effort and Brogue had to put in one jellychip worth of effort. Then their total gains from trade are 12-4=8. The Shapley division is then 4 each, which can be achieved as follows:
Aylick gets seven jellychips. Less her three units of effort, her total reward is four.
Brogue gets five jellychips. Less his one unit of effort, his total reward is four.
The Dath Ilan Child division is nine to three, which I think is only justified with the politician’s fallacy. But they are children.
AFAICT, in the Highwayman example, if the would-be robber presents his ultimatum as “give me half your silk or I burn it all,” the merchant should burn it all, same as if the robber says “give me 1% of your silk or I burn it all.” But a slightly more sophisticated highwayman might say “this is a dangerous stretch of desert, and there are many dangerous, desperate people in those dunes. I have some influence with most of the groups in the next 20 miles. For x% of your silk, I will make sure you are unmolested for that portion of your travel.” Then the merchant actually has to assign a probabilities to a bunch of events, calculate Shapley values, and roll some dice for his mixed strategy.
Covered in the glowfic. Here is how it goes down in Dath Ilan:
And in Golarion:
They just ignore the effort difference and go for 50:50 splits. Fair over the long term, robust to deception and self-deception, low cognitive effort.
The Dath Ilani kids are wrong according to Shapley Values (confirmed as the Dath Ilan philosophy here). Let’s suppose that Aylick and Brogue are paired up on a box where Aylick had to put in three jellychips worth of effort and Brogue had to put in one jellychip worth of effort. Then their total gains from trade are 12-4=8. The Shapley division is then 4 each, which can be achieved as follows:
Aylick gets seven jellychips. Less her three units of effort, her total reward is four.
Brogue gets five jellychips. Less his one unit of effort, his total reward is four.
The Dath Ilan Child division is nine to three, which I think is only justified with the politician’s fallacy. But they are children.
AFAICT, in the Highwayman example, if the would-be robber presents his ultimatum as “give me half your silk or I burn it all,” the merchant should burn it all, same as if the robber says “give me 1% of your silk or I burn it all.”
But a slightly more sophisticated highwayman might say “this is a dangerous stretch of desert, and there are many dangerous, desperate people in those dunes. I have some influence with most of the groups in the next 20 miles. For x% of your silk, I will make sure you are unmolested for that portion of your travel.”
Then the merchant actually has to assign a probabilities to a bunch of events, calculate Shapley values, and roll some dice for his mixed strategy.