Simple fair division of a square
研究了将单位正方形蛋糕通过横切和竖切进行简单分割，使得每个代理人都认为所得份额相等，证明了这种公平分割的存在性并给出了构造方法。
Suppose we are given a cake represented by the unit interval to be divided among agents evaluating the pieces of the cake by nonatomic probability measures. It is known that we can divide the unit interval into contiguous and connected pieces and assign them to the agents in such a way that the values of the pieces are equal according to the individual agents measures. Such division is said to be equitable and simple. In this paper we show that an equitable and simple division also exists in the case of dividing two-dimensional cake represented by the unit square. In this case, by simple division we mean dividing the unit square firstly by horizontal cuts, and then partition the resulting rectangles by vertical cuts. We give a method of obtaining a proportional and simple division of this cake. Furthermore, we prove the existence of proportional, equitable and simple division.