Scheduling Selfish Tasks: About the Performance of Truthful Algorithms

Abstract

This paper deals with problems which fall into the domain of selfish scheduling: a protocol is in charge of building a schedule for a set of tasks without directly knowing their length. The protocol gets these informations from agents who control the tasks. The aim of each agent is to minimize the completion time of her task while the protocol tries to minimize the maximal completion time. When an agent reports the length of her task, she is aware of what the others bid and also of the protocol's algorithm. Then, an agent can bid a false value in order to optimize her individual objective function. With erroneous information, even the most efficient algorithm may produce unreasonable solutions. An algorithm is truthful if it prevents the selfish agents from lying about the length of their task. The central question in this paper is: "How efficient a truthful algorithm can be? We study the problem of scheduling selfish tasks on parallel identical machines. This question has been raised by Christodoulou et al [8] in a distributed system, but it is also relevant in centrally controlled systems. Without considering side payments, our goal is to give a picture of the performance under the condition of truthfulness.

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

“…One has to be careful when designing a Coordination Mechanism with discontinuous functions, because the existence of equilibria is not always guaranteed 7 . It is important to emphasize, that all the mechanisms that we suggest in this paper use both lower semicontinuous and regular 8 latencies, and therefore User Equilibrium existence is guaranteed due to the theorem of [4].…”

“…Very recently, [10] considered as an objective the weighted sum of completion times. Truthful coordination mechanisms have been studied in [1,7,2].…”

Strategic Scheduling Games: Equilibria and Efficiency

“…Nevertheless many models were investigated in the literature (see for example [3,2,42,6,19,18,39] for a non exhaustive list of results), depending on several parameters: the players are either the jobs or the machines, payments are allowed or not, the strategy of an agents is vector or a singleton, pre-emption is allowed or not, etc. Here we present some results which apply for a model close to the one mainly discussed in this chapter.…”

“…We say that a mechanism (a set of m algorithms, one per machine, which allocates time windows to the players, on the basis of their declarations) is truthful (without money) if a player cannot unilaterally report a false length and decrease his completion time. The next two subsections are based on [19,18].…”

“…These include the scheduling model (preemptive mechanism) introduced in [36] and further studied in [23,20,28,9,24,46] (subsection 3.1), non-preemptive ordering mechanisms studied in [5,19,34,22] (subsection 3.2) and a brief account of mechanisms for the most general scheduling environment of unrelated machines (subsection 3.5) [34,10,14]. In section 4 we revisit nonpreemptive ordering mechanisms in the context of truthfulness [19,18], where agents may misreport their processing loads to the mechanism so as to minimize their completion time in the outcome of the game.…”