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
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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
T2 - 16th International Conference on Principles and Practice of Multi-Agent Systems, PRIMA 2013
Y2 - 1 December 2013 through 6 December 2013
ER -