A game of fair division with continuum of players
A game of fair division in the normal form
On a method of obtaining exact fair divisions
Let the unit interval I represent a cake to be divided among n players estimating the measurable subsets of I by nonatomic probability n measures. We show a method of obtaining an exact fair division of the cake such that i-th each part has i-th measure equals 1/n for all players.
On Finding Optimal Partitions of Measurable Space
We present an algorithm for finding almost optimal partitions of the unit interval [0; 1) according to given nonatomic measures 1; 2; : : : ; n. This algorithm is based on the idea of Riemann integral and the linear programming method. We also discuss the number of cuts needed for finding the optimal partitions.
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