There is well known task:
How to divide a pie between two people, so each will think that he got equal or more that the other one?
It has the following solution:
First person divide the pie on 2 equal (in his opinion) parts. Second one chooses the biggest one.
I know that it is possible to generalise in a way that N people will divide a pie on N pieces and each one will think that his part is not less than 1/N.
Is it possible to generalise this on N envy people? That means to divide a pie between N people in such a way that each one will think that his part is not less than part of any other man. In this case, when a man has got a part bigger than 1/N, he will still be following the rest of the division between the others - may be some one will get even bigger part (in this case the man will not calm down until the situation changes).
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