A Lower Bound for Scheduling Mechanisms

Christodoulou, George; Koutsoupias, Elias; Vidali, Angelina

doi:10.1007/s00453-008-9165-3

Cited by 77 publications

(107 citation statements)

References 17 publications

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“…Here we study its mechanism-design version and we improve the results of [8], where we (together with George Christodoulou) gave a lower bound of 1 + √ 2. The current work can be considered a continuation of it as we use similar tools, in particular Lemma 1; this is essentially the only known tool (used also in the seminal work of Nisan and Ronen [23]), and from this perspective it is unavoidable that we use it again here.…”

Section: Related Workmentioning

confidence: 87%

“…In this work on the other hand, we use arbitrarily many players and tasks and we obtain the bound of 1 + φ only as the limit when the number of players tends to infinity. Surprisingly, we are not using anything about the geometrical structure of the mechanism, even though it seemed as if the use of a geometric lemma was a crucial part of the proof in [8]. The main connection between the proof of the 2.61 and the 2.41 lower bound is the use of the second part of Lemma 1 which, albeit being a very simple observation seems very powerful.…”

Section: Related Workmentioning

confidence: 99%

“…The current work can be considered a continuation of it as we use similar tools, in particular Lemma 1; this is essentially the only known tool (used also in the seminal work of Nisan and Ronen [23]), and from this perspective it is unavoidable that we use it again here. However, our techniques are completely different and much more sophisticated than the ones used in [8], where we used simple instances of 3 players and 5 tasks. In this work on the other hand, we use arbitrarily many players and tasks and we obtain the bound of 1 + φ only as the limit when the number of players tends to infinity.…”

Section: Related Workmentioning

confidence: 99%

“…We recall here the definitions of the scheduling problem, of the concept of mechanisms, as well as some fundamental properties of them (see [8] for more details, references, and proofs).…”

Section: Problem Definitionmentioning

confidence: 99%

“…In particular, the only known way to take advantage of the Monotonicity Property is the following lemma [8], which will be the main ingredient of our proof. For completeness we also include the proof of this lemma.…”

Section: Problem Definitionmentioning

confidence: 99%

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A Lower Bound of 1 + φ for Truthful Scheduling Mechanisms

Koutsoupias¹,

Vidali²

Mathematical Foundations of Computer Science 2007

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Abstract. We give an improved lower bound for the approximation ratio of truthful mechanisms for the unrelated machines scheduling problem. The mechanism design version of the problem which was proposed and studied in a seminal paper of Nisan and Ronen is at the core of the emerging area of Algorithmic Game Theory. The new lower bound 1 + φ ≈ 2.618 is a step towards the final resolution of this important problem.

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Section: Related Workmentioning

confidence: 87%

Section: Related Workmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

“…We recall here the definitions of the scheduling problem, of the concept of mechanisms, as well as some fundamental properties of them (see [8] for more details, references, and proofs).…”

Section: Problem Definitionmentioning

confidence: 99%

Section: Problem Definitionmentioning

confidence: 99%

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A Lower Bound of 1 + φ for Truthful Scheduling Mechanisms

Koutsoupias¹,

Vidali²

Mathematical Foundations of Computer Science 2007

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The Pareto Frontier of Inefficiency in Mechanism Design

Filos-Ratsikas

Giannakopoulos²,

Lazos

2019

Web and Internet Economics

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We study the trade-off between the Price of Anarchy (PoA) and the Price of Stability (PoS) in mechanism design, in the prototypical problem of unrelated machine scheduling. We give bounds on the space of feasible mechanisms with respect to the above metrics, and observe that two fundamental mechanisms, namely the First-Price (FP) and the Second-Price (SP), lie on the two opposite extrema of this boundary. Furthermore, for the natural class of anonymous task-independent mechanisms, we completely characterize the PoA/PoS Pareto frontier; we design a class of optimal mechanisms SP α that lie exactly on this frontier. In particular, these mechanisms range smoothly, with respect to parameter α ≥ 1 across the frontier, between the First-Price (SP 1 ) and Second-Price (SP ∞ ) mechanisms.En route to these results, we also provide a definitive answer to an important question related to the scheduling problem, namely whether non-truthful mechanisms can provide better makespan guarantees in the equilibrium, compared to truthful ones. We answer this question in the negative, by proving that the Price of Anarchy of all scheduling mechanisms is at least n, where n is the number of machines.property, an alternative approach to the framework of Nisan and Ronen [36] is to design mechanisms that perform well in the equilibrium, i.e., they provide good PoA or PoS guarantees. This approach has been adopted, among others, by central papers in the field (e.g., see [40,43] and references therein) and is by now as much a part of algorithmic mechanism design as the original framework of [36]. An interesting question that has arisen in many settings is whether non-truthful mechanisms (evaluated at the worst-case equilibrium, in terms of their PoA) can actually outperform truthful ones (evaluated at the truth-telling, dominant strategy equilibrium), for a given objective [11,20,24].While the literature that studies the concepts of PoA and PoS is long and extensive, there seems to be a lack of a systematic approach investigating the trade-off between the two notions simultaneously. More concretely, given a problem in algorithmic mechanism design, it seems quite natural to explore not only the best mechanisms in terms of the two notions independently, but also the mechanisms that achieve the best trade-off between the two. In a sense, this approach concerns a "tighter" optimality notion, as among a set of mechanisms with an "acceptable" Price of Anarchy guarantee, we would like to identify the ones that provide the best possible Price of Stability. Our main contribution in the current paper is the proposal of such a research agenda and its application on the canonical problem in the field, introduced in the seminal work of Nisan and Ronen [36], that of scheduling on unrelated machines. Our contributionsPoA/PoS trade-off: We propose the research agenda of studying systematically the tradeoff between the Price of Anarchy and the Price of Stability in algorithmic mechanism design. Specifically, given a problem at hand and an objective function,...

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