Abstract
This paper concerns the design of mechanisms for online scheduling in which agents bid for access to a re-usable resource such as processor time or wireless network access. Each agent is assumed to arrive and depart dynamically, and in the basic model require the resource for one unit of time. We seek mechanisms that are truthful in the sense that truthful revelation of arrival, departure and value information is a dominant strategy, and that are online in the sense that they make allocation decisions without knowledge of the future. First, we provide two characterizations for the class of truthful online allocation rules. The characterizations extend beyond the typical single-parameter settings, and formalize the role of restricted misreporting in reversing existing price-based characterizations. Second, we present an online auction for unit-length jobs that achieves total value that is 2-competitive with the maximum offline value. We prove that no truthful deterministic online mechanism can achieve a better competitive ratio. Third, we consider revenue competitiveness and prove that no deterministic truthful online auction has revenue that is constant-competitive with that of the offline Vickrey-Clarke-Groves (VCG) mechanism We provide a randomized online auction that achieves a competitive ratio of O(log h), where h is the ratio of maximum value to minimum value among the agents; this mechanism does not require prior knowledge of h. Finally, we generalize our model to settings with multiple re-usable goods and to agents with different job lengths.
Highlights
1.1 MotivationOnline mechanism design concerns the design of mechanisms for markets in which agents arrive and depart over time, and the mechanism must compute allocation and payment decisions online without knowledge of the agents who will subsequently arrive
This paper concerns the design of mechanisms for online scheduling in which agents bid for access to a re-usable resource such as processor time or wireless network access
We consider revenue competitiveness and prove that no deterministic truthful online auction has revenue that is constant-competitive with that of the offline Vickrey-Clarke-Groves (VCG) mechanism We provide a randomized online auction that achieves a competitive ratio of O(log h), where h is the ratio of maximum value to minimum value among the agents; this mechanism does not require prior knowledge of h
Summary
Online mechanism design concerns the design of mechanisms for markets in which agents arrive and depart over time, and the mechanism must compute allocation and payment decisions online without knowledge of the agents who will subsequently arrive. The requirement of strategyproofness with respect to arrival and departure times makes the online auction problem difficult since it places constraints on the timing of allocations This is demonstrated by Lavi and Nisan [15], who prove that without any restriction on the types of possible misreports, it is impossible to achieve a bounded competitive ratio on efficiency. We study the problem with the assumptions of no early arrivals and no late departures, i.e., we assume that agents cannot report an arrival time earlier than their true arrival time or a departure time later than their true departure time This model was adopted by Porter [20] for his work on online auctions with re-usable goods. Almost all of our mechanisms remain strategyproof without assuming no early arrivals
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