Sequential scheduling on identical machines

Hassin, Refael; Yovel, Uri

doi:10.1016/j.orl.2015.08.003

Cited by 13 publications

(7 citation statements)

References 11 publications

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“…[15] for a network routing counterexample where the sequential price of anarchy is unbounded, while the price of anarchy is known to be 5/2 [5,14]. Indeed, subsequent to [29], for a handful of problems it was shown that the sequential price of anarchy is lower than the price of anarchy [18,20,21,29], while for some others this is exactly opposite [2,9,15].…”

Section: Motivation and Related Workmentioning

confidence: 99%

The quality of equilibria for set packing and throughput scheduling games

Jong

Uetz

2019

Int J Game Theory

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We introduce set packing games as an abstraction of situations in which n selfish players select subsets of a finite set of indivisible items, and analyze the quality of several equilibria for this class of games. Assuming that players are able to approximately play equilibrium strategies, we show that the total quality of the resulting equilibrium solutions is only moderately suboptimal. Our results are tight bounds on the price of anarchy for three equilibrium concepts, namely Nash equilibria, subgame perfect equilibria, and an equilibrium concept that we refer to as k-collusion Nash equilibrium.

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Section: Motivation and Related Workmentioning

confidence: 99%

The quality of equilibria for set packing and throughput scheduling games

Jong

Uetz

2019

Int J Game Theory

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“…For example, while the PoA is unbounded for the Unrelated Machine Scheduling game, they showed that its SPoA is bounded. In fact, positive results showing that the SPoA presents lower values than the PoA has been displayed for various games ( [5,7,8,9]). However, that is not always the case ( [10,11,12]), and we show that sequential transportation games fall in this category for all social cost functions analyzed in this paper.…”

Section: Introductionmentioning

confidence: 98%

Tight Bounds for the Price of Anarchy and Stability in Sequential Transportation Games

da Silva,

Miyazawa,

Romero

et al. 2020

Preprint

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In this paper, we analyze a transportation game first introduced by Fotakis, Gourvès, and Monnot in 2017, where players want to be transported to a common destination as quickly as possible and, in order to achieve this goal, they have to choose one of the available buses. We introduce a sequential version of this game and provide bounds for the Sequential Price of Stability and the Sequential Price of Anarchy in both metric and non-metric instances, considering three social cost functions: the total traveled distance by all buses, the maximum distance traveled by a bus, and the sum of the distances traveled by all players (a new social cost function that we introduce). Finally, we analyze the Price of Stability and the Price of Anarchy for this new function in simultaneous transportation games.

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“…• Hassin and Yovel [23] consider machine scheduling and focus on the special case of related machines. The authors prove that for this model, the SPoA is at most 2 while the PoA is Θ(ln n/ ln ln n).…”

Section: Introductionmentioning

confidence: 99%

The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

et al. 2019

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This paper provides new bounds on the quality of equilibria in finite congestion games with affine cost functions, specifically for atomic network routing games. It is well known that the price of anarchy equals exactly 5/2 in general. For symmetric network routing games, it is at most (5n − 2)/(2n + 1), where n is the number of players. This paper answers to two open questions for congestion games. First, we show that the price of anarchy bound (5n − 2)/(2n + 1) is tight for symmetric network routing games, thereby answering a decade-old open question. Second, we ask whether sequential play and subgame perfection allows to evade worst-case Nash equilibria, and thereby reduces the price of anarchy. This is motivated by positive results for congestion games with a small number of players, as well as recent results for other resource allocation problems. Our main result is the perhaps surprising proof that subgame perfect equilibria of sequential symmetric network routing games with linear cost functions can have an unbounded price of anarchy. We complete the picture by analyzing the case with two players: we show that the sequential price of anarchy equals 7/5 and that computing the outcome of a subgame perfect equilibrium is NP-hard.

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Sequential scheduling on identical machines

Cited by 13 publications

References 11 publications

The quality of equilibria for set packing and throughput scheduling games

The quality of equilibria for set packing and throughput scheduling games

Tight Bounds for the Price of Anarchy and Stability in Sequential Transportation Games

The Inefficiency of Nash and Subgame Perfect Equilibria for Network Routing

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