| 无嫉妒蛋糕分配中的谎言 |
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| 引用本文： | 彭晓芸,陶永芊. 无嫉妒蛋糕分配中的谎言[J]. 计算机工程与应用, 2017, 53(22): 55-60. DOI: 10.3778/j.issn.1002-8331.1703-0233 |
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| 作者姓名： | 彭晓芸 陶永芊 |
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| 作者单位： | 1.江西省税务干部学校，南昌 3300292.南昌大学 数学系，南昌 330031 |
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| 摘 要： | 对于给定的任意一个蛋糕分配算法，研究了玩家能从谎报中获取多大的利益。考虑两种类型的玩家：风险寻求玩家和风险厌恶玩家，并且把玩家的价值密度函数限制为分段常数。证明了风险寻求玩家和风险厌恶玩家均不能从谎报中获取更多利益。但如果只允许算法在蛋糕上切[n-1]刀，证明了玩家通过谎报能够拿到多出[Θ(n)]倍的利益。
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| 关 键 词： | 蛋糕分配 无嫉妒 风险寻求 风险厌恶 |
Misreporting in envy-free cake cutting |
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| PENG Xiaoyun,TAO Yongqian. Misreporting in envy-free cake cutting[J]. Computer Engineering and Applications, 2017, 53(22): 55-60. DOI: 10.3778/j.issn.1002-8331.1703-0233 |
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| Authors: | PENG Xiaoyun TAO Yongqian |
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| Affiliation: | 1.Jiangxi Tax Cadre School, Nanchang 330029, China2.Department of Mathematics, Nanchang University, Nanchang 330031, China |
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| Abstract: | It is studied that how much benefit an agent can obtain by his misreport in any envy-free cake cutting algorithm. Two types of agents, risk-seeking and risk-averse, are considered, and the value density function is restricted to piecewise constant. It can be showed that an agent cannot be benefited by misreporting if he is risk-seeking or risk-averse. If considering allocations with only [n-1] cuts on the cake, the utility gain from misreporting can be as much as [Θ(n)]. |
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| Keywords: | cake cutting envy-free risk-seeking risk-averse |
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