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 |
|---|---|
| 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) |
|---|---|
| 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 |
|---|---|
| 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
Strategy-proof mechanisms for the k-winner selection problem. / Sakurai, Yuko; Okimoto, Tenda; Oka, Masaaki; Yokoo, Makoto.
PRIMA 2013: Principles and Practice of Multi-Agent Systems - 16th International Conference, Proceedings. 2013. p. 292-307 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8291 LNAI).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
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 -