Sharing Non-anonymous Costs of Multiple Resources Optimally

Klimm, Max; Schmand, Daniel

doi:10.1007/978-3-319-18173-8_20

Cited by 17 publications

(10 citation statements)

References 25 publications

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“…Our problem belongs to the topic of network cost-sharing and hedonic coalition formation problems [7]- [16]. A study particularly related to our results is the price of anarchy for stable matching and the various extensions to K-sized coalitions [17], [18].…”

Section: Related Workmentioning

confidence: 82%

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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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Section: Related Workmentioning

confidence: 82%

“…This paper presents a comprehensive study for the SPoA of a general model of coalition formation, considering various arXiv:1511.05270v4 [cs.GT] 16 Oct 2017 common fair cost-sharing mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Chau

Elbassioni

2018

IEEE Trans. Control Netw. Syst.

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“…Kollias and Roughgarden [17] showed how the Shapley value cost-sharing method can be applied to restore pure equilibria, whereas Gopalakrishnan et al [18] showed that the more general class of generalized weighted Shapley values are the only ones that can guarantee this property. The price of anarchy of the induced games has been the subject of extensive study, with examples including those in [19][20][21][22][23][24]. Authors who used cost-sharing to improve the efficiency of equilibria include Chen et al [25], who focused on the price of stability, and von Falkenhausen and Harks [26], who provided an approach which requires knowledge of the instance at hand.…”

Section: Related Workmentioning

confidence: 99%

Equilibrium Inefficiency and Computation in Cost-Sharing Games in Real-Time Scheduling Systems

2021

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We study cost-sharing games in real-time scheduling systems where the server’s activation cost in every time slot is a function of its load. We focus on monomial cost functions and consider both the case when the degree is less than one (inducing positive congestion effect for the jobs) and when it is greater than one (inducing negative congestion effect for the jobs). For the former case, we provide tight bounds on the price of anarchy, and show that the price of anarchy grows to infinity as a polynomial of the number of jobs in the game. For the latter, we observe that existing results provide constant and tight (asymptotically in the degree of the monomial) bounds on the price of anarchy. We then turn to analyze payment mechanism with arbitrary cost-sharing, that is, when the strategy of a player includes also its payment. We show that our mechanism reduces the price of anarchy of games with n jobs and unit server costs from Θ(n) to 2. We also show that, for a restricted class of instances, a similar improvement is achieved for monomial server costs. This is not the case, however, for unrestricted instances of monomial costs, for which we prove that the price of anarchy remains super-constant for our mechanism. For systems with load-independent activation costs, we show that our mechanism can produce an optimal solution which is stable against coordinated deviations.

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“…Chen, Roughgarden and Valiant [23] were the first to study the design aspects for this game, identifying the best protocol with respect to the PoA and PoS in various cases, followed by [62] for parallel links, [40,43,54] for weighted congestion games, [29,47,59] for network games, [41] for routing games and [52] for resource allocation. The Bayesian Price of anarchy was first studied in auctions by [26]; see also [58] for routing games, and [61] for the PoS of Shapley protocol in cost-sharing games.…”

Section: Related Workmentioning

confidence: 99%

Designing Cost-Sharing Methods for Bayesian Games

2017

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We study the design of cost-sharing protocols for two fundamental resource allocation problems, the Set Cover and the Steiner Tree Problem, under environments of incomplete information (Bayesian model). Our objective is to design protocols where the worst-case Bayesian Nash equilibria have low cost, i.e. the Bayesian Price of Anarchy (PoA) is minimized. Although budget balance is a very natural requirement, it puts considerable restrictions on the design space, resulting in high PoA. We propose an alternative, relaxed requirement called budget balance in the equilibrium (BBiE). We show an interesting connection between algorithms for Oblivious Stochastic optimization problems and cost-sharing design with low PoA. We exploit this connection for both problems and we enforce approximate solutions of the stochastic problem, as Bayesian Nash equilibria, with the same guarantees on the PoA. More interestingly, we show how to obtain the same bounds on the PoA, by using anonymous posted prices which are desirable

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Sharing Non-anonymous Costs of Multiple Resources Optimally

Cited by 17 publications

References 25 publications

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Quantifying Inefficiency of Fair Cost-Sharing Mechanisms for Sharing Economy

Equilibrium Inefficiency and Computation in Cost-Sharing Games in Real-Time Scheduling Systems

Designing Cost-Sharing Methods for Bayesian Games

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