Contention Issues in Congestion Games

Koutsoupias, Elias; Papakonstantinopoulou, Katia

doi:10.1007/978-3-642-31585-5_55

Cited by 11 publications

(7 citation statements)

References 20 publications

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“…Here we extend the selfish routing model by incorporating a temporal component into the problem formulation. Other attempts to address this issue include [21,19,13,24], but none of these results discuss coordination mechanisms using strongly local (decentralized) policies.…”

Section: Our Contributions and Techniquesmentioning

confidence: 99%

“…However they lack an important aspect of real network routing which is the fact that routing happens over time, and any realistic model should take this into account. To address this issue, several new models have been proposed to capture the nature of realistic routing over time [10,11,21,19,24,13,12,4]. Amongst these models, the concept of coordination mechanisms, first introduced in an influential paper by Christodoulou, Koutsoupias, and Nanavati [10], have been proposed to capture the queueing nature of routing.…”

Section: Introductionmentioning

confidence: 99%

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Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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Abstract. While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first coordination mechanisms with provable price of anarchy for this problem. Interestingly, we achieve our price of anarchy results using simple and strongly local policies such as Shortest Job First and the Smith's Rule (also called HDF). In particular, for the case of unweighted jobs, we design a coordination mechanism with polylogarithmic price of anarchy. For weighted jobs, on the other hand, we show that price of anarchy is a function of the depth of the tree and accompany this result by a lower bound for the price of anarchy for the Smith Rule policy and other common strongly local scheduling policies. Our price of anarchy results also imply improved approximation algorithms for the underlying optimization problem of routing over a tree. This problem is well motivated from applications of routing in supercomputers and data center networks where average sojourn time is an important metric.

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Section: Our Contributions and Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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“…There has been also research on pricing schemes [25] as well as on cases in which the channel quality changes dynamically with time and players must choose their transmission levels accordingly [19,26,4]. An interesting game-theoretic model that lies between the contention and congestion model was studied in [16]; where decisions of when to submit is part of the action space of the players.…”

Section: Other Related Workmentioning

confidence: 99%

A 3-Player Protocol Preventing Persistence in Strategic Contention with Limited Feedback

Christodoulou

Gairing

Nikoletseas

et al. 2017

Algorithmic Game Theory

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In this paper, we study contention resolution protocols from a game-theoretic perspective. In a recent work [7], we considered acknowledgment-based protocols, where a user gets feedback from the channel only when she attempts transmission. In this case she will learn whether her transmission was successful or not. One of the main results of [7] was that no acknowledgment-based protocol can be in equilibrium. In fact, it seems that many natural acknowledgment-based protocols fail to prevent users from unilaterally switching to persistent protocols that always transmit with probability 1. It is therefore natural to ask how powerful a protocol must be so that it can beat persistent deviators. In this paper we consider age-based protocols, which can be described by a sequence of probabilities of transmitting in each time step. Those probabilities are given beforehand and do not change based on the transmission history. We present a 3-player age-based protocol that can prevent users from unilaterally deviating to a persistent protocol in order to decrease their expected transmission time. It is worth noting that the answer to this question does not follow from the results and proof ideas of [7]. Our protocol is non-trivial, in the sense that, when all players use it, finite expected transmission time is guaranteed. In fact, we show that this protocol is preferable to any deadline protocol in which, after some fixed time, attempt transmission with probability 1 in every subsequent step. An advantage of our protocol is that it is very simple to describe, and users only need a counter to keep track of time. Whether there exist n-player age-based protocols that do not use counters and can prevent persistence is left as an open problem for future research.

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“…We study the temporal routing games in the framework of coordination mechanisms [18]. Unlike congestion games, which were also studied in the context of selfish routing, the temporal routing games model the queueing nature of routing in real networks and has been an active area of research in recent years [20,28,6,15,21,8,9]. The specific model we consider is the following: Given a graph G = (V, E) and a set of packets, each packet has a size p j , a weight or priority w j , and wants to travel from some source h j ∈ V to some destination o j ∈ V .…”

Section: ) Coordination Mechanisms For Temporal Routingmentioning

confidence: 99%

Robust Price of Anarchy Bounds via LP and Fenchel Duality

Kulkarni¹,

Mirrokni²

2014

Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms

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Bounding the price of anarchy (PoA), which quantifies the degradation in the quality of outcomes in a (pure) Nash equilibrium of a game, is one of the fundamental questions in computational game theory. However, for a large class of games, a pure NE may not always exist and hence a natural question to pursue is to quantify the inefficiency for weaker notions of equilibrium such as mixed Nash equilibrium, correlated equilibrium or coarse correlated equilibrium, all of which are known to exist for finite games. Several techniques have been developed for bounding the price of anarchy, yet, only a handful of them are applicable for proving the PoA bounds for general equilibrium concepts. Most notable among such techniques is Roughgarden's elegant smoothness framework, which led to the concept of robust price of anarchy. The term refers to the inefficiency bounds applicable to general equilibrium notions such as coarse correlated equilibrium.In this paper, we develop a new framework based on LP and Fenchel duality for bounding the robust price of anarchy for a large class of games. We use our framework to give the first PoA bounds for temporal routing games on graphs and energy minimization games in machine scheduling. Most notably, we present the first coordination mechanisms with bounded PoA for temporal routing over general graphs, show a related lowerbound result, and an improved bound on the price of stability for this game. Previously, coordination mechanisms with bounded PoA were only known for restricted classes of graphs such as trees or parallel edges. Furthermore, we demonstrate the wide applicability of our framework by giving new proofs of the PoA bounds for three classical games -weighted affine congestion games, competitive facility location games and simultaneous second price auctions. Our price anarchy bounds for these games match the ones known in the literature or obtained using the smoothness framework.All our proofs use the following technique: we first show that for a wide class of games, one can formulate the underlying optimization problem as a linear (or convex) program such that the (Fenchel) dual of the relaxation encodes the equilibrium condition. Further, the dual program has a specific structure with variables for players and resources, which can be naturally interpreted as the cost incurred by the players and the congestion of the resource in an equilibrium outcome. This lets us argue that our definition of dual variables satisfy the dual constraints and using the weak duality theorem we establish the PoA bounds.

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Contention Issues in Congestion Games

Cited by 11 publications

References 20 publications

Coordination Mechanisms for Selfish Routing over Time on a Tree

Coordination Mechanisms for Selfish Routing over Time on a Tree

A 3-Player Protocol Preventing Persistence in Strategic Contention with Limited Feedback

Robust Price of Anarchy Bounds via LP and Fenchel Duality

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