Resource-Aware Protocols for Network Cost-Sharing Games

Christodoulou, George C.; Gkatzelis, Vasilis; Latifian, Mohamad; Sgouritsa, Alkmini

doi:10.1145/3391403.3399528

Cited by 3 publications

(9 citation statements)

References 42 publications

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“…So, how can the mechanism approximate the optimal solution without knowing ? Prior work focused on the case of concave or convex cost functions, and designed mechanisms leveraging the fact that the corresponding optimal assignments are reasonably "well behaved": for concave costs there always exists an optimal solution where all the jobs are assigned to a single machine, and for convex costs an optimal assignment can be reached using a simple greedy solution (e.g., [8,9]). However, we cannot expect to find such convenient structural properties when dealing with the vast family of bounded functions, because the optimal assignment can change radically as a function of .…”

Section: Our Resultsmentioning

confidence: 99%

“…In subsequent work, Christodoulou et al [9] designed resource-aware mechanisms for the same class of scheduling games that we study in this paper, and were able to achieve a constant PoA for instances with convex and concave cost functions. In a recent paper, Christodoulou et al [8] extended many of these results to more general graphs, beyond parallel links, including directed acyclic or series parallel graphs with convex or concave cost functions on the edges.…”

Section: Related Workmentioning

confidence: 99%

“…Our mechanisms, as well as many mechanisms in the related work (e.g. [8,9,24]), use a global ordering over the universe N of players in deciding how to distribute the cost. Although the externality of the users in the games that we study is symmetric (e.g., they all cause the same marginal increase in the cost of a machine), the mechanism needs to share the cost unevenly among them to achieve a good PoA 5 .…”

Section: Preliminariesmentioning

confidence: 99%

“…Then, it is easy to check that, regarding the overcharging, each enforcer may "cause" some regular agent to pay at most the cost of the outcome of the Delayed-OPT algorithm and each enforcer itself may pay some arbitrarily small value . 8 For the sake of contradiction suppose that in some Nash equilibrium there exist machines < such that machine is used and machine is not full. Let be the largest possible such index.…”

Section: Warm-up: a Class Of Capacitated Constant Functionsmentioning

confidence: 99%

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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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Section: Our Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

Section: Warm-up: a Class Of Capacitated Constant Functionsmentioning

confidence: 99%

See 2 more Smart Citations

Resource-Aware Cost-Sharing Mechanisms with Priors

Gkatzelis

Pountourakis

Sgouritsa

2021

Proceedings of the 22nd ACM Conference on Economics and Computation

Self Cite

View full text Add to dashboard Cite

show abstract

“…So, how can the mechanism approximate the optimal solution without knowing n? Prior work focused on the case of concave or convex cost functions, and designed mechanisms leveraging the fact that the corresponding optimal assignments are reasonably "well behaved": for concave costs there always exists an optimal solution where all the jobs are assigned to a single machine, and for convex costs an optimal assignment can be reached using a simple greedy solution (e.g., Christodoulou et al [2017Christodoulou et al [ , 2020). However, we cannot expect to find such convenient structural properties when dealing with the vast family of bounded functions, because the optimal assignment can change radically as a function of n.…”

Section: Our Resultsmentioning

confidence: 99%

Resource-Aware Cost-Sharing Mechanisms with Priors

Gkatzelis¹,

Pountourakis²,

Sgouritsa³

2021

Preprint

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In a decentralized system with m 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.

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Improved Price of Anarchy via Predictions

Gkatzelis¹,

Kollias²,

Sgouritsa³

et al. 2022

Preprint

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A central goal in algorithmic game theory is to analyze the performance of decentralized multiagent systems, like communication and information networks. In the absence of a central planner who can enforce how these systems are utilized, the users can strategically interact with the system, aiming to maximize their own utility, possibly leading to very inefficient outcomes, and thus a high price of anarchy. To alleviate this issue, the system designer can use decentralized mechanisms that regulate the use of each resource (e.g., using local queuing protocols or scheduling mechanisms), but with only limited information regarding the state of the system. These information limitations have a severe impact on what such decentralized mechanisms can achieve, so most of the success stories in this literature have had to make restrictive assumptions (e.g., by either restricting the structure of the networks or the types of cost functions).In this paper, we overcome some of the obstacles that the literature has imposed on decentralized mechanisms, by designing mechanisms that are enhanced with predictions regarding the missing information. Specifically, inspired by the big success of the literature on "algorithms with predictions", we design decentralized mechanisms with predictions and evaluate their price of anarchy as a function of the prediction error, focusing on two very well-studied classes of games: scheduling games and multicast network formation games.

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Resource-Aware Protocols for Network Cost-Sharing Games

Cited by 3 publications

References 42 publications

Resource-Aware Cost-Sharing Mechanisms with Priors

Resource-Aware Cost-Sharing Mechanisms with Priors

Resource-Aware Cost-Sharing Mechanisms with Priors

Improved Price of Anarchy via Predictions

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