TY - JOUR

T1 - Auctioning time

T2 - Truthful auctions of heterogeneous divisible goods

AU - Aumann, Yonatan

AU - Dombb, Yair

AU - Hassidim, Avinatan

N1 - Publisher Copyright:
© 2015 ACM.

PY - 2015/12/1

Y1 - 2015/12/1

N2 - We consider the problem of auctioning time - a one-dimensional continuously-divisible heterogeneous good - among multiple agents. Applications include auctioning time for using a shared device, auctioning TV commercial slots, and more. Different agents may have different valuations for the different possible intervals; the goal is to maximize the aggregate utility. Agents are self-interested and may misrepresent their true valuation functions if this benefits them. Thus, we seek auctions that are truthful. Considering the case that each agent may obtain a single interval, the challenge is twofold, as we need to determine both where to slice the interval, and who gets what slice. We consider two settings: discrete and continuous. In the discrete setting, we are given a sequence of m indivisible elements (e1, ⋯, em), and the auction must allocate each agent a consecutive subsequence of the elements. In the continuous setting, we are given a continuous, infinitely divisible interval, and the auction must allocate each agent a subinterval. The agents' valuations are nonatomic measures on the interval. We show that, for both settings, the associated computational problem is NP-complete even under very restrictive assumptions. Hence, we provide approximation algorithms. For the discrete case, we provide a truthful auctioning mechanism that approximates the optimal welfare to within a logmfactor. The mechanism works for arbitrary monotone valuations. For the continuous setting, we provide a truthful auctioning mechanism that approximates the optimal welfare to within an O(log n) factor (where n is the number of agents). Additionally, we provide a truthful 2-approximation mechanism for the case that all pieces must be of some fixed size.

AB - We consider the problem of auctioning time - a one-dimensional continuously-divisible heterogeneous good - among multiple agents. Applications include auctioning time for using a shared device, auctioning TV commercial slots, and more. Different agents may have different valuations for the different possible intervals; the goal is to maximize the aggregate utility. Agents are self-interested and may misrepresent their true valuation functions if this benefits them. Thus, we seek auctions that are truthful. Considering the case that each agent may obtain a single interval, the challenge is twofold, as we need to determine both where to slice the interval, and who gets what slice. We consider two settings: discrete and continuous. In the discrete setting, we are given a sequence of m indivisible elements (e1, ⋯, em), and the auction must allocate each agent a consecutive subsequence of the elements. In the continuous setting, we are given a continuous, infinitely divisible interval, and the auction must allocate each agent a subinterval. The agents' valuations are nonatomic measures on the interval. We show that, for both settings, the associated computational problem is NP-complete even under very restrictive assumptions. Hence, we provide approximation algorithms. For the discrete case, we provide a truthful auctioning mechanism that approximates the optimal welfare to within a logmfactor. The mechanism works for arbitrary monotone valuations. For the continuous setting, we provide a truthful auctioning mechanism that approximates the optimal welfare to within an O(log n) factor (where n is the number of agents). Additionally, we provide a truthful 2-approximation mechanism for the case that all pieces must be of some fixed size.

KW - Auctions

KW - Cake cutting

KW - Resource allocation

UR - http://www.scopus.com/inward/record.url?scp=85031933903&partnerID=8YFLogxK

U2 - 10.1145/2833086

DO - 10.1145/2833086

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SN - 2167-8375

VL - 4

JO - ACM Transactions on Economics and Computation

JF - ACM Transactions on Economics and Computation

IS - 1

M1 - 3

ER -