### Abstract

The cake cutting problem is concerned with the fair allocation of a divisible good among agents whose preferences vary 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 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 such real-world resources 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-proof mechanisms that satisfy Pareto efficiency, which are based on the serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose a heuristic-based allocation 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 abandons Pareto efficiency, we develop an envy-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.

Original language | English |
---|---|

Pages (from-to) | 41-61 |

Number of pages | 21 |

Journal | Fundamenta Informaticae |

Volume | 158 |

Issue number | 1-3 |

DOIs | |

Publication status | Published - Jan 1 2018 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Algebra and Number Theory
- Information Systems
- Computational Theory and Mathematics

### Cite this

*Fundamenta Informaticae*,

*158*(1-3), 41-61. https://doi.org/10.3233/FI-2018-1641

**Strategy-proof Cake Cutting Mechanisms for All-or-nothing Utility.** / Ihara, Takamasa; Tsuruta, Shunsuke; Todo, Taiki; Sakurai, Yuko; Yokoo, Makoto.

Research output: Contribution to journal › Article

*Fundamenta Informaticae*, vol. 158, no. 1-3, pp. 41-61. https://doi.org/10.3233/FI-2018-1641

}

TY - JOUR

T1 - Strategy-proof Cake Cutting Mechanisms for All-or-nothing Utility

AU - Ihara, Takamasa

AU - Tsuruta, Shunsuke

AU - Todo, Taiki

AU - Sakurai, Yuko

AU - Yokoo, Makoto

PY - 2018/1/1

Y1 - 2018/1/1

N2 - The cake cutting problem is concerned with the fair allocation of a divisible good among agents whose preferences vary 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 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 such real-world resources 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-proof mechanisms that satisfy Pareto efficiency, which are based on the serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose a heuristic-based allocation 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 abandons Pareto efficiency, we develop an envy-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.

AB - The cake cutting problem is concerned with the fair allocation of a divisible good among agents whose preferences vary 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 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 such real-world resources 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-proof mechanisms that satisfy Pareto efficiency, which are based on the serial dictatorship mechanism, at the sacrifice of envy-freeness. To address computational feasibility, we propose a heuristic-based allocation 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 abandons Pareto efficiency, we develop an envy-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.

UR - http://www.scopus.com/inward/record.url?scp=85047940301&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047940301&partnerID=8YFLogxK

U2 - 10.3233/FI-2018-1641

DO - 10.3233/FI-2018-1641

M3 - Article

AN - SCOPUS:85047940301

VL - 158

SP - 41

EP - 61

JO - Fundamenta Informaticae

JF - Fundamenta Informaticae

SN - 0169-2968

IS - 1-3

ER -