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Questions tagged [fair-division]

For various problems related to dividing a resource among several parties.

Fair division, also known as the cake-cutting problem, the sandwich-splitting problem, and the pizza-dividing problem, is the problem of dividing a resource in such a way that all recipients believe that they have received a fair amount.

Various versions of this problems appear as logical puzzles in recreational mathematics.

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Challenge: "Dividing" a number above 0 and ending up with the same, or a greater number (creative task)

Here's a question/challenge for those of you who know quite a bit about math, or enjoy to be creative with what you do know (just for reference: I'm virtually illiterate when it comes to any math more advanced than the basic basics, and you're…
Chris Smith
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How to solve this problem? Distributed Game theory?

I have this problem: We dispose of some resources, say $\{f_1, f_2, \dotsc, f_m\}$; We have some agents or players, say $\{\mathrm{p}_1, \mathrm{p}_2, \dotsc, \mathrm{p}_n\}$; Every player has some utility $u_i$; If two player or more $(u_i,…
zighalo
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Fair three-way sandwich division

This question discusses fair three-way sandwich division. Mentoined solutions include the Selfridge–Conway discrete procedure and the moving-knife procedure. I posed the question to the guys at the office and we can't think why this method would…
Daniel
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Thoughts about a how to share a cake

So when i was a kid we used to do this thing when we shared a snack. one kid would cut the snack in half and the other would pick which of the two halfs he wants. this way, even though the picker will always have a slight edge, the cut would be…
DAcheese
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Which practicable solutions exist to fair distribution of a finite resource over a finite time horizon?

Imagine we have $X$ amount of some resource available over a fixed, known, and finite time period $T$. An unknown but finite number $N$ of users can each at arbitrary times request some share $Y = y/X$ of the resource $X$. We do not know in advance…
Thomas Arildsen
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Allowance distribution problem

When I say allowance, I mean like the kind you earned as a child. Here is the problem I am trying to solve. A parent has $20 they want to give to the child for doing all of their chores. If the child does all of their chores, they get 100% of their…
Nathan Clark
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Understanding Austin's two moving knives procedure for cutting a cake fairly

From wikipedia description, the Austin procedure goes as follows Alice places one knife on the left of the cake and a second parallel to it on the right where she judges it splits the cake in two. Alice moves both knives to the right in a way that…
markeb
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Fair turn sequence for 6 (or n≥3) players, when we care who goes after whom

My searching has come up with, at best, this question: What's the fairest turn sequence for n players? which as far as I can tell does not answer my question. I have a game with 6 players - let's call them A, B, C, D, E and F. My goal is to create a…
NeatNit
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MIP programming for fairness

I have a MIP model that allocates 24 rides between 6 drivers (with many constraints irrelevant here), and an important part of my objective is splitting the rides fairly. The easiest implementation I could think of is to punish for any driver that…
ihadanny
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Spherical Cake and the egg slicer

Recently I baked a spherical cake (3cm radius) and invited over a few friends, 6 of them, for dinner. When done with main course, I thought of serving this spherical cake and to avoid uninvited disagreements over the size of the shares, I took my…
user356774
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Fairness problem

I need to figure it out how without exceeding the use of the number 10, find three different ways of distributing some blue and red marbles in a container, so that the probability of randomly choosing two marbles of the same color will equal that…
TAQ
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Maximal cake-cutting

Alice and George divide a cake between them. The cake is a 1-dimensional interval and both players value the entire cake as 1. The valuations of the players are represented by non-atomic measures on the cake. The following division procedure is…
Erel Segal-Halevi
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Is my cake split envy-free (and coalition-resistant)?

I once read that splitting a cake in 4 parts envy-free is notoriouse difficult. Not to mention splitting it with 5 or more people. Methods involve arbitrarily long recursions and cake split onto molecular scale. I was thinking about the…
Dorus
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Weighted division with min and max bound?

Let's say I have 10,000 dollars I want divided among 10 people. With simple division each person gets $1,000. Easy enough. Now suppose each person has a share in a company. I want to divide the money base on their percentage of their shares in…
saeed khoshbakht
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For 2 people, division of good s is equitable, why following statement is true?

As I said, For 2 people, division of goods is equitable, then One of the following is true 1) The division is envy free 2) If they switch their shares, then the division is envy free. I started by assuming that It is envy-free and tried to prove…
Daniel
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