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Strategy-Proof Cake Cutting Mechanisms for All-or-Nothing Utility

  • Takamasa Ihara
  • Shunsuke Tsuruta
  • Taiki Todo
  • Yuko Sakurai
  • Makoto Yokoo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9387)

Abstract

The cake cutting problem must fairly allocate a divisible good among agents who have varying preferences over it. Recently, designing strategy-proof cake cutting mechanisms has caught considerable attention from AI and MAS researchers. Previous works assumed that an agent’s utility function is additive so that theoretical analysis becomes tractable. However, in practice, agents have non-additive utility functions over a resource. In this paper, we consider the all-or-nothing utility function as a representative example of non-additive utility because it can widely cover agents’ preferences for real-world resources, such as the usage of meeting rooms, time slots for computational resources, bandwidth usage, and so on. We first show the incompatibility between envy-freeness and Pareto efficiency when each agent has all-or-nothing utility. We next propose two strategy-proofmechanisms that satisfy Pareto efficiency, which are based on a serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose an approximation algorithm to find a near-optimal allocation in time polynomial in the number of agents, since the problem of finding a Pareto efficient allocation is NP-hard. As another approach that abandon Pareto efficiency, we develop anenvy-free mechanism and show that one of our serial dictatorship based mechanisms satisfies proportionality in expectation, which is a weaker definition of proportionality. Finally, we evaluate the efficiency obtained by our proposed mechanisms by computational experiments.

Keywords

Utility Function Reference Interval Approximate Algorithm Require Length Allocation Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Takamasa Ihara
    • 1
  • Shunsuke Tsuruta
    • 1
  • Taiki Todo
    • 1
  • Yuko Sakurai
    • 1
  • Makoto Yokoo
    • 1
  1. 1.Kyushu UniversityFukuokaJapan

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