575 research outputs found
Routing Games with Progressive Filling
Max-min fairness (MMF) is a widely known approach to a fair allocation of
bandwidth to each of the users in a network. This allocation can be computed by
uniformly raising the bandwidths of all users without violating capacity
constraints. We consider an extension of these allocations by raising the
bandwidth with arbitrary and not necessarily uniform time-depending velocities
(allocation rates). These allocations are used in a game-theoretic context for
routing choices, which we formalize in progressive filling games (PFGs).
We present a variety of results for equilibria in PFGs. We show that these
games possess pure Nash and strong equilibria. While computation in general is
NP-hard, there are polynomial-time algorithms for prominent classes of
Max-Min-Fair Games (MMFG), including the case when all users have the same
source-destination pair. We characterize prices of anarchy and stability for
pure Nash and strong equilibria in PFGs and MMFGs when players have different
or the same source-destination pairs. In addition, we show that when a designer
can adjust allocation rates, it is possible to design games with optimal strong
equilibria. Some initial results on polynomial-time algorithms in this
direction are also derived
EGOIST: Overlay Routing Using Selfish Neighbor Selection
A foundational issue underlying many overlay network applications ranging from routing to P2P file sharing is that of connectivity management, i.e., folding new arrivals into an existing overlay, and re-wiring to cope with changing network conditions. Previous work has considered the problem from two perspectives: devising practical heuristics for specific applications designed to work well in real deployments, and providing abstractions for the underlying problem that are analytically tractable, especially via game-theoretic analysis. In this paper, we unify these two thrusts by using insights gleaned from novel, realistic theoretic models in the design of Egoist â a prototype overlay routing system that we implemented, deployed, and evaluated on PlanetLab. Using measurements on PlanetLab and trace-based simulations, we demonstrate that Egoist's neighbor selection primitives significantly outperform existing heuristics on a variety of performance metrics, including delay, available bandwidth, and node utilization. Moreover, we demonstrate that Egoist is competitive with an optimal, but unscalable full-mesh approach, remains highly effective under significant churn, is robust to cheating, and incurs minimal overhead. Finally, we discuss some of the potential benefits Egoist may offer to applications.National Science Foundation (CISE/CSR 0720604, ENG/EFRI 0735974, CISE/CNS 0524477, CNS/NeTS 0520166, CNS/ITR 0205294; CISE/EIA RI 0202067; CAREER 04446522); European Commission (RIDS-011923
cISP: A Speed-of-Light Internet Service Provider
Low latency is a requirement for a variety of interactive network
applications. The Internet, however, is not optimized for latency. We thus
explore the design of cost-effective wide-area networks that move data over
paths very close to great-circle paths, at speeds very close to the speed of
light in vacuum. Our cISP design augments the Internet's fiber with free-space
wireless connectivity. cISP addresses the fundamental challenge of
simultaneously providing low latency and scalable bandwidth, while accounting
for numerous practical factors ranging from transmission tower availability to
packet queuing. We show that instantiations of cISP across the contiguous
United States and Europe would achieve mean latencies within 5% of that
achievable using great-circle paths at the speed of light, over medium and long
distances. Further, we estimate that the economic value from such networks
would substantially exceed their expense
The complexity of pure nash equilibria in max-congestion games
We study Network Max-Congestion Games (NMC games, for short), a
class of network games where each player tries to minimize the most congested
edge along the path he uses as strategy. We focus our study on the complexity
of computing a pure Nash equilibria in this kind of games. We show that, for
single-commodity games with non-decreasing delay functions, this problem
is in P when either all the paths from the source to the target node are
disjoint or all the delay functions are equal. For the general case, we prove
that the computation of a PNE belongs to the complexity class PLS through a
new technique based on generalized ordinal potential functions and a slightly
modified definition of the usual local search neighborhood. We further apply
this technique to a different class of games (which we call Pareto-efficient)
with restricted cost functions. Finally, we also prove some PLS-hardness
results, showing that computing a PNE for Pareto-efficient NMC games is
indeed a PLS-complete problem
Social Network Games with Obligatory Product Selection
Recently, Apt and Markakis introduced a model for product adoption in social
networks with multiple products, where the agents, influenced by their
neighbours, can adopt one out of several alternatives (products). To analyze
these networks we introduce social network games in which product adoption is
obligatory.
We show that when the underlying graph is a simple cycle, there is a
polynomial time algorithm allowing us to determine whether the game has a Nash
equilibrium. In contrast, in the arbitrary case this problem is NP-complete. We
also show that the problem of determining whether the game is weakly acyclic is
co-NP hard.
Using these games we analyze various types of paradoxes that can arise in the
considered networks. One of them corresponds to the well-known Braess paradox
in congestion games. In particular, we show that social networks exist with the
property that by adding an additional product to a specific node, the choices
of the nodes will unavoidably evolve in such a way that everybody is strictly
worse off.Comment: In Proceedings GandALF 2013, arXiv:1307.416
Smoothed Efficient Algorithms and Reductions for Network Coordination Games
Worst-case hardness results for most equilibrium computation problems have
raised the need for beyond-worst-case analysis. To this end, we study the
smoothed complexity of finding pure Nash equilibria in Network Coordination
Games, a PLS-complete problem in the worst case. This is a potential game where
the sequential-better-response algorithm is known to converge to a pure NE,
albeit in exponential time. First, we prove polynomial (resp. quasi-polynomial)
smoothed complexity when the underlying game graph is a complete (resp.
arbitrary) graph, and every player has constantly many strategies. We note that
the complete graph case is reminiscent of perturbing all parameters, a common
assumption in most known smoothed analysis results.
Second, we define a notion of smoothness-preserving reduction among search
problems, and obtain reductions from -strategy network coordination games to
local-max-cut, and from -strategy games (with arbitrary ) to
local-max-cut up to two flips. The former together with the recent result of
[BCC18] gives an alternate -time smoothed algorithm for the
-strategy case. This notion of reduction allows for the extension of
smoothed efficient algorithms from one problem to another.
For the first set of results, we develop techniques to bound the probability
that an (adversarial) better-response sequence makes slow improvements on the
potential. Our approach combines and generalizes the local-max-cut approaches
of [ER14,ABPW17] to handle the multi-strategy case: it requires a careful
definition of the matrix which captures the increase in potential, a tighter
union bound on adversarial sequences, and balancing it with good enough rank
bounds. We believe that the approach and notions developed herein could be of
interest in addressing the smoothed complexity of other potential and/or
congestion games
Atomic dynamic flow games : adaptive versus nonadaptive agents
We propose a game model for selfish routing of atomic agents, who compete for use of a network to travel from their origins to a common destination as fast as possible. We follow a frequently used rule that the latency an agent experiences on each edge is a constant transit time plus a variable waiting time in a queue. A key feature that differentiates our model from related ones is an edge-based tie-breaking rule for prioritizing agents in queueing when they reach an edge at the same time. We study both nonadaptive agents (each choosing a one-off origin-destination path simultaneously at the very beginning) and adaptive ones (each making an online decision at every nonterminal vertex they reach as to which next edge to take). On the one hand, we constructively prove that a (pure) Nash equilibrium (NE) always exists for nonadaptive agents, and show that every NE is weakly Pareto optimal and globally first-in-first-out. We present efficient algorithms for finding an NE and best responses of nonadaptive agents. On the other hand, we are among the first to consider adaptive atomic agents, for which we show that a subgame perfect equilibrium (SPE) always exists, and that each NE outcome for nonadaptive agents is an SPE outcome for adaptive agents, but not vice versa
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