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)].

Key words: cake cutting, envy-free, risk-seeking, risk-averse

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。

关键词: 蛋糕分配, 无嫉妒, 风险寻求, 风险厌恶