Improvements for Truthful Mechanisms with Verifiable One-Parameter Selfish Agents

Abstract

In this paper we study optimization problems with verifiable one-parameter selfish agents introduced by Auletta et al. [ICALP 2004]. Our goal is to allocate load among the agents, provided that the secret data of each agent is a single positive rational number: the cost they incur per unit load. In such a setting the payment is given after the load completion, therefore if a positive load is assigned to an agent, we are able to verify if the agent declared to be faster than she actually is. We design truthful mechanisms when the agents’ type sets are upper-bounded by a finite value. We provide a truthful mechanism that is c ·(1 + ?)-approximate if the underlying algorithm is c-approximate and weakly-monotone. Moreover, if type sets are also discrete, we provide a truthful mechanism preserving the approximation ratio of the used algorithm. Our results improve the existing ones which provide truthful mechanisms dealing only with finite type sets and do not preserve the approximation ratio of the underlying algorithm. Finally we give a full characterization of the Q||C max problem by using only our results. Even if our payment schemes need upper-bounded type sets, every instance of Q||C max can be ”mapped” into an instance with upper-bounded type sets preserving the approximation ratio.

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