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In this chapter, we will study the problem ofCake cutting cutting or dividing a cake (a metaphor for any limited and perfectly divisible resource like land or time) fairly among a group of individuals who may have different preferences over different portions of the cake. In Sect. 15.1, we will first present the cake-cutting problem formally and, in Sect. 15.2, we will introduce three notions of fairness, namely proportionality, envy-freeness, and equitability, along with the relations between some of these three notions. In Sect. 15.3, we will present protocols that produce a proportional cake division among two, three, or arbitrary number of individuals and, in Sect. 15.4, we will present protocols that produce an envy-free cake division among three individuals.

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Cake Cutting and Fairness

  • 章节

  • 发表日期：

    2025年

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  • Ismail Saglam

摘要

In this chapter, we will study the problem ofCake cutting cutting or dividing a cake (a metaphor for any limited and perfectly divisible resource like land or time) fairly among a group of individuals who may have different preferences over different portions of the cake. In Sect. 15.1, we will first present the cake-cutting problem formally and, in Sect. 15.2, we will introduce three notions of fairness, namely proportionality, envy-freeness, and equitability, along with the relations between some of these three notions. In Sect. 15.3, we will present protocols that produce a proportional cake division among two, three, or arbitrary number of individuals and, in Sect. 15.4, we will present protocols that produce an envy-free cake division among three individuals.