Cake-cutting

Symmetric fair cake-cutting

Symmetric fair cake-cutting is a variant of the fair cake-cutting problem, in which fairness is applied not only to the final outcome, but also to the assignment of roles in the division procedure. As an example, consider a birthday cake that has to be divided between two children with different tastes, such that each child feels that his/her share is "fair", i.e., worth at least 1/2 of the entire cake. They can use the classic divide and choose procedure: Alice cuts the cake into two pieces worth exactly 1/2 in her eyes, and George chooses the piece that he considers more valuable. The outcome is always fair. However, the procedure is not symmetric: while Alice always gets a value of exactly 1/2 of her value, George may get much more than 1/2 of his value. Thus, while Alice does not envy George's share, she does envy George's role in the procedure. In contrast, consider the alternative procedure in which Alice and George both make half-marks on the cake, i.e., each of them marks the location in which the cake should be cut such that the two pieces are equal in his/her eyes. Then, the cake is cut exactly between these cuts—if Alice's cut is a and George's cut is g, then the cake is cut at (a+g)/2. If aWikipedia).

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Introduction to Fair Division

This video introduced fair division. Site: http://mathispower4u.com

From playlist Fair Division

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How To Split A Cake Fairly Using Math

How can 2 people split up a cake, knowing that each person wants to get a larger piece than the other? What about 3 people, or even N people? This is an example of a fair division problem from game theory. There are many cake-cutting algorithms to produce a fair solution mathematically. In

From playlist Everyday Math

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Ryuhei Uehara - Design Schemes for Fair Dice - G4G13 April 2018

A cube is used as a fair die of 6 faces. However, there are many dice of different shapes on the market. To make them fair, most of them usually have some symmetric shapes. I classify these variants of dice on the market into two groups. First, let's consider that a sphere as a model of a

From playlist G4G13 Videos

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Part 2 - http://www.youtube.com/watch?v=SaBI6IjIGy0

From playlist Tutorials

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Fair Division: The Last Diminisher Method

This video explains and provides an example of the last diminisher method of fair division. Site: http://mathispower4u.com

From playlist Fair Division

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Fair Division: The Sealed Bid Method

This video explains and provides examples of how to apply the sealed bid method. Site: http://mathispower4u.com

From playlist Fair Division

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Fair Division: The Moving Knife Method

This video explains and provides an example of the moving knife method. Site: http://mathispower4u.com

From playlist Fair Division

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More resources available at www.misterwootube.com

From playlist Further Work with Functions

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Equally sharing a cake between three people - Numberphile

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From playlist Women in Mathematics - Numberphile

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Princess Cake Solution

Mathematics of Fair Distribution using the Lone-Chooser Method. This example invloves a cake being shared by three players. Recall, that the cake is a metaphor for any continuously divisible item

From playlist Discrete Math

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From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes

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From playlist Algebra for Kids

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From playlist Taiji

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Fair Division: The Divider-Chooser Method

The video explains the divider-chooser method of fair division. Site: http://mathispower4u.com

From playlist Fair Division

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NIPS 2011 Learning Semantics Workshop: Learning Semantics of Movement

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Related pages

Envy-free matching | Proportional cake-cutting | Bipartite graph | Subgame perfect equilibrium | Fair cake-cutting | Deterministic algorithm | Even–Paz protocol | Divide and choose | Envy-free cake-cutting | Lone divider