### Abstract

The goal of this paper is to develop a strategy-proof (SP) mechanism for the k-winner selection problem, which finds a set of (at most) k winners among participants. Here, we assume the winners can have positive/negative externalities with each other; the gross utility of a winner not only depends on whether she wins, but also on the other winners. If the types of agents, i.e., the gross utilities of agents, are known, we can obtain a Pareto efficient (PE) allocation that maximizes the sum of the gross utilities of winners in polynomial time, assuming k is a constant. On the other hand, when the types of agents are private information, we need a mechanism that can elicit the true types of agents; it must satisfy SP. We first show that there exists no SP mechanism that is PE, individual rational (IR), and non-deficit (ND) in a general setting where we put no restrictions on possible agent types. Thus, we need to give up at least one of these desirable properties. Next, we examine how a family of Vickrey-Clarke-Groves (VCG) based mechanisms works for this problem. We consider two alternative VCG-based mechanisms in this setting, both of which are SP and PE. We show that one alternative, called VCG-ND, is ND but not IR, and the other alternative, called VCG-IR, is IR but not ND. Also, we show special cases where VCG-ND satisfies IR, or VCG-IR satisfies ND. Moreover, we propose mechanisms called VCG-ND+ and VCG-IR+, which can be applied to a general setting, where a mechanism designer has partial knowledge about the possible interactions among agents. Both VCG-ND+ and VCG-IR+ are SP, IR, and ND, but they are not PE. Finally, we present a concise graphical representation scheme of agant types.

Original language | English |
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Title of host publication | PRIMA 2013 |

Subtitle of host publication | Principles and Practice of Multi-Agent Systems - 16th International Conference, Proceedings |

Pages | 292-307 |

Number of pages | 16 |

DOIs | |

Publication status | Published - Dec 1 2013 |

Event | 16th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2013 - Dunedin, New Zealand Duration: Dec 1 2013 → Dec 6 2013 |

### 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 | 8291 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 16th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2013 |
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Country | New Zealand |

City | Dunedin |

Period | 12/1/13 → 12/6/13 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*PRIMA 2013: Principles and Practice of Multi-Agent Systems - 16th International Conference, Proceedings*(pp. 292-307). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8291 LNAI). https://doi.org/10.1007/978-3-642-44927-7_20

**Strategy-proof mechanisms for the k-winner selection problem.** / Sakurai, Yuko; Okimoto, Tenda; Oka, Masaaki; Yokoo, Makoto.

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

*PRIMA 2013: Principles and Practice of Multi-Agent Systems - 16th International Conference, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8291 LNAI, pp. 292-307, 16th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2013, Dunedin, New Zealand, 12/1/13. https://doi.org/10.1007/978-3-642-44927-7_20

}

TY - GEN

T1 - Strategy-proof mechanisms for the k-winner selection problem

AU - Sakurai, Yuko

AU - Okimoto, Tenda

AU - Oka, Masaaki

AU - Yokoo, Makoto

PY - 2013/12/1

Y1 - 2013/12/1

N2 - The goal of this paper is to develop a strategy-proof (SP) mechanism for the k-winner selection problem, which finds a set of (at most) k winners among participants. Here, we assume the winners can have positive/negative externalities with each other; the gross utility of a winner not only depends on whether she wins, but also on the other winners. If the types of agents, i.e., the gross utilities of agents, are known, we can obtain a Pareto efficient (PE) allocation that maximizes the sum of the gross utilities of winners in polynomial time, assuming k is a constant. On the other hand, when the types of agents are private information, we need a mechanism that can elicit the true types of agents; it must satisfy SP. We first show that there exists no SP mechanism that is PE, individual rational (IR), and non-deficit (ND) in a general setting where we put no restrictions on possible agent types. Thus, we need to give up at least one of these desirable properties. Next, we examine how a family of Vickrey-Clarke-Groves (VCG) based mechanisms works for this problem. We consider two alternative VCG-based mechanisms in this setting, both of which are SP and PE. We show that one alternative, called VCG-ND, is ND but not IR, and the other alternative, called VCG-IR, is IR but not ND. Also, we show special cases where VCG-ND satisfies IR, or VCG-IR satisfies ND. Moreover, we propose mechanisms called VCG-ND+ and VCG-IR+, which can be applied to a general setting, where a mechanism designer has partial knowledge about the possible interactions among agents. Both VCG-ND+ and VCG-IR+ are SP, IR, and ND, but they are not PE. Finally, we present a concise graphical representation scheme of agant types.

AB - The goal of this paper is to develop a strategy-proof (SP) mechanism for the k-winner selection problem, which finds a set of (at most) k winners among participants. Here, we assume the winners can have positive/negative externalities with each other; the gross utility of a winner not only depends on whether she wins, but also on the other winners. If the types of agents, i.e., the gross utilities of agents, are known, we can obtain a Pareto efficient (PE) allocation that maximizes the sum of the gross utilities of winners in polynomial time, assuming k is a constant. On the other hand, when the types of agents are private information, we need a mechanism that can elicit the true types of agents; it must satisfy SP. We first show that there exists no SP mechanism that is PE, individual rational (IR), and non-deficit (ND) in a general setting where we put no restrictions on possible agent types. Thus, we need to give up at least one of these desirable properties. Next, we examine how a family of Vickrey-Clarke-Groves (VCG) based mechanisms works for this problem. We consider two alternative VCG-based mechanisms in this setting, both of which are SP and PE. We show that one alternative, called VCG-ND, is ND but not IR, and the other alternative, called VCG-IR, is IR but not ND. Also, we show special cases where VCG-ND satisfies IR, or VCG-IR satisfies ND. Moreover, we propose mechanisms called VCG-ND+ and VCG-IR+, which can be applied to a general setting, where a mechanism designer has partial knowledge about the possible interactions among agents. Both VCG-ND+ and VCG-IR+ are SP, IR, and ND, but they are not PE. Finally, we present a concise graphical representation scheme of agant types.

UR - http://www.scopus.com/inward/record.url?scp=84893072924&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893072924&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-44927-7_20

DO - 10.1007/978-3-642-44927-7_20

M3 - Conference contribution

AN - SCOPUS:84893072924

SN - 9783642449260

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

SP - 292

EP - 307

BT - PRIMA 2013

ER -