Strong equilibrium in cost sharing connection games

Epstein, Amir; Feldman, Michal; Mansour, Yishay

doi:10.1145/1250910.1250924

Cited by 53 publications

(28 citation statements)

References 20 publications

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“…They showed that for the unrelated machine scheduling games the Strong Price of Anarchy is at most 2m − 1, where m is the number of machines and that strong equilibria always exist. Later, Epstein et al [10] showed that the Strong Price of Anarchy of cost sharing games is Hn = O(log n), same as our bound for Subgame Perfect Equilibria. Strong Equilibria assume collective rationality, and requires players to collaborate, while Spe assumes only individual rationality.…”

Section: Introductionsupporting

confidence: 74%

The curse of simultaneity

Leme

Syrgkanis

Tardos

2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

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Typical models of strategic interactions in computer science use simultaneous move games. However, in applications simultaneity is often hard or impossible to achieve. In this paper, we study the robustness of the Nash Equilibrium when the assumption of simultaneity is dropped. In particular we propose studying the sequential price of anarchy: the quality of outcomes of sequential versions of games whose simultaneous counterparts are prototypical in algorithmic game theory. We study different classes of games with high price of anarchy, and show that the subgame perfect equilibrium of their sequential version is a much more natural prediction, ruling out unreasonable equilibria, and leading to much better quality solutions.We consider three examples of such games: Cost Sharing Games, Unrelated Machine Scheduling Games and Consensus Games. For Machine Cost Sharing Games, the sequential price of anarchy is at most O(log(n)), an exponential improvement of the O(n) price of anarchy of their simultaneous counterparts. Further, the subgame perfect equilibrium can be computed by a polynomial time greedy algorithm, and is independent of the order the players arrive. For Unrelated Machine Scheduling Games we show that the sequential price of anarchy is bounded as a function of the number of jobs n and machines m (by at most O(m2 n )), while in the simultaneous version the price of anarchy is unbounded even for two players and two machines. For Consensus Games we observe that the optimal outcome for generic weights is the unique equilibrium that arises in the sequential game. We also study the related Cut Games, where we show that the *

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Section: Introductionsupporting

confidence: 74%

The curse of simultaneity

Leme

Syrgkanis

Tardos

2012

Proceedings of the 3rd Innovations in Theoretical Computer Science Conference

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“…In particular, our model is a special case of a K-capacitated network cost-sharing game with a simple structure of n parallel links and non-anonymous cost functions such that a strategy profile of the users in the network game corresponds to a coalition structure 2 . However, the key difference of our model from those in [7], [11], [15] is that we consider replaceable resources from a large pool of available resources, such that a subset of deviating users can always form a new coalition, independent from other users. This is not true in general network cost-sharing games, when there are limited resources (e.g., links) that a deviating coalition of players can utilize, and it may not be possible to form arbitrary coalitions independent from others.…”

Section: Related Workmentioning

confidence: 99%

“…It is also worth mentioning how our results of usage based cost-sharing relate to cost-sharing with anonymous cost functions in network design games [7] or connection games [11]. On one hand, our model is simpler as we do not assume connectivity requirements in a network, but only an abstract setting that allows arbitrary coalitions up to a certain capacity (but we allow non-anonymous cost functions).…”

Section: Related Workmentioning

confidence: 99%

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Chau

Elbassioni

2018

IEEE Trans. Control Netw. Syst.

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Sharing economy is a distributed peer-to-peer economic paradigm, which gives rise to a variety of social interactions for economic purposes. One fundamental distributed decision-making process is coalition formation for sharing certain replaceable resources collaboratively, for example, sharing hotel rooms among travelers, sharing taxi-rides among passengers, and sharing regular passes among users. Motivated by the applications of sharing economy, this paper studies a coalition formation game subject to the capacity of K participants per coalition. The participants in each coalition are supposed to split the associated cost according to a given cost-sharing mechanism. A stable coalition structure is established when no group of participants can opt out to form another coalition that leads to lower individual payments. We quantify the inefficiency of distributed decision-making processes under a cost-sharing mechanism by the strong price of anarchy (SPoA), comparing a worst-case stable coalition structure and a social optimum. In particular, we derive SPoA for common fair cost-sharing mechanisms (e.g., equal-split, proportional-split, egalitarian and Nash bargaining solutions of bargaining games, and usage based cost-sharing). We show that the SPoA for equal-split, proportional-split, and usage based costsharing (under certain conditions) is Θ(log K), whereas the one for egalitarian and Nash bargaining solutions is O( √ K log K). Therefore, distributed decision-making processes under common fair cost-sharing mechanisms induce only moderate inefficiency.

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“…For example, [27] showed that in a network formation game with single-source and multiple-targets played on a network that is not an SPP network, there is no strong PNE. [15] showed that in a game on an SPP network there always exist a strong PNE. Moreover, [20] showed that in network formation games, even if a strong PNE exists, not every beneficial coordinated deviations sequence converges to one.…”

Section: Conclusion and Open Problemsmentioning

confidence: 99%

The Efficiency of Best-Response Dynamics

Feldman

Snappir

Tamir

2017

Algorithmic Game Theory

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Best response (BR) dynamics is a natural method by which players proceed toward a pure Nash equilibrium via a local search method. The quality of the equilibrium reached may depend heavily on the order by which players are chosen to perform their best response moves. A deviator rule S is a method for selecting the next deviating player. We provide a measure for quantifying the performance of different deviator rules. The inefficiency of a deviator rule S is the maximum ratio, over all initial profiles p, between the social cost of the worst equilibrium reachable by S from p and the social cost of the best equilibrium reachable from p. This inefficiency always lies between 1 and the price of anarchy.We study the inefficiency of various deviator rules in network formation games and job scheduling games (both are congestion games, where BR dynamics always converges to a pure NE). For some classes of games, we compute optimal deviator rules. Furthermore, we define and study a new class of deviator rules, called local deviator rules. Such rules choose the next deviator as a function of a restricted set of parameters, and satisfy a natural condition called independence of irrelevant players. We present upper bounds on the inefficiency of some local deviator rules, and also show that for some classes of games, no local deviator rule can guarantee inefficiency lower than the price of anarchy. * A preliminary version appears in the proc.

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Strong equilibrium in cost sharing connection games

Cited by 53 publications

References 20 publications

The curse of simultaneity

The curse of simultaneity

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

The Efficiency of Best-Response Dynamics

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