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

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4answers
47 views

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 ...
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1answer
40 views

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 ...
2
votes
2answers
97 views

Protocol to split a common item between 2 people

I have a question related to the "pizza splitting" problem (split the pizza in a fair way), and I am looking for an answer of hopefully the same elegance (first splits, second chooses). Not sure if ...
1
vote
1answer
52 views

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 ...
370
votes
25answers
50k views

Splitting a sandwich and not feeling deceived

This is a problem that has haunted me for more than a decade. Not all the time - but from time to time, and always on windy or rainy days, it suddenly reappears in my mind, stares at me for half an ...
2
votes
1answer
68 views

Fair Division: Making the Differences in Players' Valuations Believable

When teaching basic fair division algorithms, the students always propose some simple and (at the first glance) correct solutions for $n$ players, which unfortunately are not correct! The only way I ...
6
votes
1answer
99 views

Fair division of an octagon

A land-plot belongs to two partners. Its form is a regular octagon with area 1. They want to divide it such that one gets area $p$ and one gets area $1-p$, where $p \in (0,1)$ is a given constant. ...
2
votes
1answer
127 views

Lyapunov Theorem for beginners

I study the subject of fair division (cake-cutting), and many papers contain a reference to a theorem by Lyapunov, which states that the range of any real-valued, non-atomic vector measure is compact ...
0
votes
1answer
29 views

Partition set to contain the same number of elements distributing the remainder

Given $|B| = 23$ and number of partitions $P=4$. We want to partition the given set $B = B_1\cup\dots\cup B_P$ so that every partition $B_i$ contains the same amount of elements where the remaining ...
1
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1answer
110 views

Weighted division?

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 score on a test from 0 to 200. Now I want ...
0
votes
2answers
100 views

A beer problem (divide bills)

I am making an application to divide bills. I have the following problem: Jhon and Paul were to a pub , and they consumed 20 beers. James get in the bar and they consumed ten more beers. How much ...
4
votes
4answers
358 views

Cutting the cake problem if the value measures are not finitely additive

Background I have (rather recently) dabbled in game theory. I need it to design an algorithm to share chores. Obviously this is a kind of cake-cutting problem. So far, I have fought my way through An ...
1
vote
3answers
109 views

How to derive the share of a prize given scores

I am curious to find out reasonable ways of dividing a prize among $n$ people in the following situation: To make the example specific, we have $6$ people in total who are going to share a prize of ...
2
votes
1answer
174 views

Evenly dividing candy bar into $n$ pieces

I have 2 friends. We have one candybar and we want to divide it evenly. Unfortunately we don't have any way of accurately measuring and cutting the candybar. Therefore we are looking for a method ...
1
vote
1answer
94 views

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 ...
4
votes
6answers
2k views

Cutting the Cake Problem

The tradition way for two children to divide a piece of cake fairly between them is "you cut, I choose", What process accomplishes this is intuitively clear. Is there a similar process which works for ...
16
votes
8answers
4k views

Is it possible to 'split' coin flipping 3 ways?

When flipping a coin to make important decisions in life you can flip once to choose between 2 possible outcomes. (Heads I eat cake, Tails I eat chocolate!) You can also flip twice to choose between ...