LOGO Fair Division MATHEMATICS IN DAILY LIFE Hua Yinglei Hu Zhihao Fan Xin Si Peiyu

Assign Tasks Amidakuji Tasks Divide Tasks

How to divide a cake? --two persons Taking more things into consideration

Proportional Division

The Final Reduction Algorithm Person who is the last one to cut the 1/n part will get this part of cake Everyone has two choices: Give the cut-cake to the next one directly Cut down the size of the piece into 1/n according to his valuation

If anyone cuts the cake into piece which is smaller than 1/n of the cake deliberately…… If anyone gives a piece of cake which is bigger than 1/n of the cake to someone else deliberately……

Selfridge-Conway Algorithm B P1 divides the cake into three pieces he considers of equal sizes …… P2 P1 P3

Applications and Conclusions Fair division is the problem of dividing a set of goods between several people, such that each person receives his/her due share. Distribution of social welfare 1 Divorce settlements 2 Airport traffic management and so on 3

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