### 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 allor-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-proof mechanisms 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 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 |
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Title of host publication | PRIMA 2015 |

Subtitle of host publication | Principles and Practice of Multi-Agent Systems - 18th International Conference, Proceedings |

Editors | Paolo Torroni, Andrea Omicini, Jane Hsu, Qingliang Chen, Paolo Torroni, Andrea Omicini, Jane Hsu, Qingliang Chen, Serena Villata, Serena Villata |

Publisher | Springer Verlag |

Pages | 118-133 |

Number of pages | 16 |

ISBN (Print) | 9783319255231, 9783319255231 |

DOIs | |

Publication status | Published - Jan 1 2015 |

Event | 18th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2015 - Bertinoro, Italy Duration: Oct 26 2015 → Oct 30 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9387 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 18th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2015 |
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Country | Italy |

City | Bertinoro |

Period | 10/26/15 → 10/30/15 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*PRIMA 2015: Principles and Practice of Multi-Agent Systems - 18th International Conference, Proceedings*(pp. 118-133). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9387). Springer Verlag. https://doi.org/10.1007/978-3-319-25524-8_8

**Strategy-proof cake cutting mechanisms for all-or-nothing utility.** / Ihara, Takamasa; Tsuruta, Shunsuke; Todo, Taiki; Sakurai, Yuko; Yokoo, Makoto.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*PRIMA 2015: Principles and Practice of Multi-Agent Systems - 18th International Conference, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9387, Springer Verlag, pp. 118-133, 18th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2015, Bertinoro, Italy, 10/26/15. https://doi.org/10.1007/978-3-319-25524-8_8

}

TY - GEN

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 - 2015/1/1

Y1 - 2015/1/1

N2 - 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 allor-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-proof mechanisms 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 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 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 allor-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-proof mechanisms 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 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=84950311112&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950311112&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-25524-8_8

DO - 10.1007/978-3-319-25524-8_8

M3 - Conference contribution

SN - 9783319255231

SN - 9783319255231

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 118

EP - 133

BT - PRIMA 2015

A2 - Torroni, Paolo

A2 - Omicini, Andrea

A2 - Hsu, Jane

A2 - Chen, Qingliang

A2 - Torroni, Paolo

A2 - Omicini, Andrea

A2 - Hsu, Jane

A2 - Chen, Qingliang

A2 - Villata, Serena

A2 - Villata, Serena

PB - Springer Verlag

ER -