Designing Cost-Sharing Methods for Bayesian Games

Christodoulou, George; Leonardi, Stefano; Sgouritsa, Alkmini

doi:10.1007/s00224-017-9832-3

Cited by 8 publications

(6 citation statements)

References 70 publications

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“…More general separable protocols have been studied mostly in terms of the price of anarchy, e.g., for scheduling (or matroid games) [6,13,19,24,53] or single-source network design with [20,21] and without uncertainty [17]. The best result here is a price of anarchy (and stability) of 2 via Prim-Sharing [17], a protocol inspired by Prim's MST algorithm.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

Efficient Black-Box Reductions for Separable Cost Sharing

et al. 2021

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In cost-sharing games with delays, a set of agents jointly uses a subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a nonshareable player-specific delay for each resource. A separable cost-sharing protocol determines cost shares that are budget-balanced, separable, and guarantee existence of pure Nash equilibria (PNE). We provide black-box reductions reducing the design of such a protocol to the design of an approximation algorithm for the underlying cost-minimization problem. In this way, we obtain separable cost-sharing protocols in matroid games, single-source connection games, and connection games on n-series-parallel graphs. All these reductions are efficiently computable - given an initial allocation profile, we obtain a cheaper profile and separable cost shares turning the profile into a PNE. Hence, in these domains, any approximation algorithm yields a separable cost-sharing protocol with price of stability bounded by the approximation factor.

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Section: Preliminaries and Related Workmentioning

confidence: 99%

Efficient Black-Box Reductions for Separable Cost Sharing

et al. 2021

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“…The cost-sharing mechanism is aware of this stochastic process, so they designed a mechanism that leverages this information to achieve a constant PoA. Following-up on this work Christodoulou et al [11] extended the constant PoA to also include Bayesian Nash equilibria.…”

Section: Related Workmentioning

confidence: 99%

Resource-Aware Cost-Sharing Mechanisms with Priors

Gkatzelis

Pountourakis

Sgouritsa

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

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In a decentralized system with machines, we study the selfish scheduling problem where each user strategically chooses which machine to use. Each machine incurs a cost, which is a function of the total load assigned to it, and some cost-sharing mechanism distributes this cost among the machine's users. The users choose a machine aiming to minimize their own share of the cost, so the cost-sharing mechanism induces a game among them. We approach this problem from the perspective of a designer who can select which cost-sharing mechanism to use, aiming to minimize the price of anarchy (PoA) of the induced games.Recent work introduced the class of resource-aware cost-sharing mechanisms, whose decisions can depend on the set of machines in the system, but are oblivious to the total number of users. These mechanisms can guarantee low PoA bounds for instances where the cost functions of the machines are all convex or concave, but can suffer from very high PoA for cost functions that deviate from these families.In this paper we show that if we enhance the class of resource-aware mechanisms with some prior information regarding the users, then they can achieve low PoA for a much more general family of cost functions. We first show that, as long as the mechanism knows just two of the participating users, then it can assign special roles to them and ensure a constant PoA. We then extend this idea to settings where the mechanism has access to the probability with which each user is present in the system. For all these instances, we provide a mechanism that achieves an expected PoA that is logarithmic in the expected number of users.CCS Concepts: • Theory of computation Quality of equilibria; Algorithmic game theory.

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“…More general separable protocols have been studied mostly in terms of the price of anarchy, e.g., for scheduling (or matroid games) [6,13,19,24,52] or single-source network design with [20,21] and without uncertainty [17]. The best result here is a price of anarchy (and stability) of 2 via Prim-Sharing [17], a protocol inspired by Prim's MST algorithm.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

Efficient Black-Box Reductions for Separable Cost Sharing

Harks¹,

Hoefer²,

Huber³

et al. 2018

Preprint

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In cost sharing games with delays, a set of agents jointly allocates a finite subset of resources. Each resource has a fixed cost that has to be shared by the players, and each agent has a nonshareable player-specific delay for each resource. A prominent example is uncapacitated facility location (UFL), where facilities need to be opened (at a shareable cost) and clients want to connect to opened facilities. Each client pays a cost share and his non-shareable physical connection cost. Given any profile of subsets allocated by the agents, a separable cost sharing protocol determines cost shares that satisfy budget balance on every resource and separability over the resources. Moreover, a separable protocol guarantees existence of pure Nash equilibria in the induced strategic game for the agents.In this paper, we study separable cost sharing protocols in several general combinatorial domains. We provide black-box reductions to reduce the design of a separable cost-sharing protocol to the design of an approximation algorithm for the underlying cost minimization problem. In this way, we obtain new separable cost-sharing protocols in games based on arbitrary playerspecific matroids, single-source connection games without delays, and connection games on nseries-parallel graphs with delays. All these reductions are efficiently computable -given an initial allocation profile, we obtain a cheaper profile and separable cost shares turning the profile into a pure Nash equilibrium. Hence, in these domains any approximation algorithm can be used to obtain a separable cost sharing protocol with a price of stability bounded by the approximation factor.

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Designing Cost-Sharing Methods for Bayesian Games

Cited by 8 publications

References 70 publications

Efficient Black-Box Reductions for Separable Cost Sharing

Efficient Black-Box Reductions for Separable Cost Sharing

Resource-Aware Cost-Sharing Mechanisms with Priors

Efficient Black-Box Reductions for Separable Cost Sharing

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