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Thou Shalt Not Covet Thy Neighbor's Cake

The main mathematical news

2016:  Aziz and Mackenzie found a solution of the envy-free cake-cutting problem for n people in a bounded number of steps.

2015: Aziz and Mackenzie found a solution of the envy-free cake-cutting problem for 4 people in a bounded number of steps.

1995:  Brams and Taylor found a solution of the envy-free cake-cutting problem for n people in an unbounded number of steps.

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Additional Theorems / conjectures / Open questions
  • Two methods for fair division: The Last Diminisher; The Moving Knife
  • Selfridge-Conway procedure for envy-free division of a cake among 3 people
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The main mathematical concepts / Principles

Game theory (MSC2010#97K99)

*  Resource allocation

*  Fair division

*  Envy-free division

*  Upper/lower bound

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