Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya, Sayan; Kulkarni, Janardhan; Mirrokni, Vahab

doi:10.1007/978-3-662-43948-7_16

Cited by 8 publications

(20 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our result implies that PoA is independent of number packets and depends solely on structure of the network. Previous known results for this problem could only handle restricted topologies such as tree networks [9] or parallel links [21,8]. Further, our result matches the tight robust PoA bound of 4 for HDF policy obtained by Cole et al in [21] using smoothness framework and generalizes the results in [8,9] to CCE.…”

Section: ) Coordination Mechanisms For Temporal Routingsupporting

confidence: 86%

“…Previous known results for this problem could only handle restricted topologies such as tree networks [9] or parallel links [21,8]. Further, our result matches the tight robust PoA bound of 4 for HDF policy obtained by Cole et al in [21] using smoothness framework and generalizes the results in [8,9] to CCE. Constant-factor approximation algorithms can be inferred from the works of [29,30] for the underlying optimization problem in the offline setting, however, no analysis of local forwarding policies (such as HDF) are known.…”

Section: ) Coordination Mechanisms For Temporal Routingsupporting

confidence: 86%

“…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%

See 2 more Smart Citations

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: ) Coordination Mechanisms For Temporal Routingsupporting

confidence: 86%

Section: ) Coordination Mechanisms For Temporal Routingsupporting

confidence: 86%

Section: ) Coordination Mechanisms For Temporal Routingmentioning

confidence: 99%

See 1 more Smart Citation

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…Similar to our context, the designer has to decide in advance game-specific policies, without knowing the exact input. Such mechanisms have been used for scheduling problems under the objective of minimising the makespan [2,7,16,49,53] or minimising the sum of players' costs [1,9,33], as well as for simple routing games [10,28].…”

Section: Related Workmentioning

confidence: 99%

Designing Cost-Sharing Methods for Bayesian Games

2017

View full text Add to dashboard Cite

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

show abstract

“…The designer has to decide in advance local scheduling policies or increases in edge latencies, without knowing the exact input, and has been used for scheduling problems [24,39,42,8,18,26,12,1,2] as well as for simple routing games [25,13].…”

Section: Example 12 (Generalized Weighted Shapley)mentioning

confidence: 99%

Designing Networks with Good Equilibria under Uncertainty

Christodoulou¹,

Sgouritsa

2015

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

View full text Add to dashboard Cite

We consider the problem of designing network costsharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree.We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model).In the adversarial model, the goal of the designer is to choose a single, universal cost-sharing protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design?We first demonstrate that there exist classes of graphs where knowledge of the underlying metric can dramatically improve the performance of good network cost-sharing design. For outerplanar graph metrics, we provide a universal cost-sharing protocol with constant PoA, in contrast to protocols that, by ignoring the graph metric, cannot achieve PoA better than Ω(log k). Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of Ω(log k), which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes.Then we switch to the stochastic model, where each player is independently activated according to some probability distribution that is known to the * Department of Computer Science, University of Liverpool, UK. Email:gchristo@liverpool.ac.uk. This work was supported by EP/M008118/1, EP/K01000X/1 and LT140046.† Department of Computer Science, University of Liverpool, UK. Email:salkmini@liverpool.ac.uk designer. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol that achieves constant PoA. We remark, that the first result holds also for the black-box model, where the probabilities are not known to the designer, but is allowed to draw independent (polynomially many) samples.

show abstract

Coordination Mechanisms for Selfish Routing over Time on a Tree

Cited by 8 publications

References 32 publications

Robust Price of Anarchy Bounds via LP and Fenchel Duality

Robust Price of Anarchy Bounds via LP and Fenchel Duality

Designing Cost-Sharing Methods for Bayesian Games

Designing Networks with Good Equilibria under Uncertainty

Contact Info

Product

Resources

About