230 research outputs found
Selfish Network Creation with Non-Uniform Edge Cost
Network creation games investigate complex networks from a game-theoretic
point of view. Based on the original model by Fabrikant et al. [PODC'03] many
variants have been introduced. However, almost all versions have the drawback
that edges are treated uniformly, i.e. every edge has the same cost and that
this common parameter heavily influences the outcomes and the analysis of these
games.
We propose and analyze simple and natural parameter-free network creation
games with non-uniform edge cost. Our models are inspired by social networks
where the cost of forming a link is proportional to the popularity of the
targeted node. Besides results on the complexity of computing a best response
and on various properties of the sequential versions, we show that the most
general version of our model has constant Price of Anarchy. To the best of our
knowledge, this is the first proof of a constant Price of Anarchy for any
network creation game.Comment: To appear at SAGT'1
Strategic Network Formation with Attack and Immunization
Strategic network formation arises where agents receive benefit from
connections to other agents, but also incur costs for forming links. We
consider a new network formation game that incorporates an adversarial attack,
as well as immunization against attack. An agent's benefit is the expected size
of her connected component post-attack, and agents may also choose to immunize
themselves from attack at some additional cost. Our framework is a stylized
model of settings where reachability rather than centrality is the primary
concern and vertices vulnerable to attacks may reduce risk via costly measures.
In the reachability benefit model without attack or immunization, the set of
equilibria is the empty graph and any tree. The introduction of attack and
immunization changes the game dramatically; new equilibrium topologies emerge,
some more sparse and some more dense than trees. We show that, under a mild
assumption on the adversary, every equilibrium network with agents contains
at most edges for . So despite permitting topologies denser
than trees, the amount of overbuilding is limited. We also show that attack and
immunization don't significantly erode social welfare: every non-trivial
equilibrium with respect to several adversaries has welfare at least as that of
any equilibrium in the attack-free model.
We complement our theory with simulations demonstrating fast convergence of a
new bounded rationality dynamic which generalizes linkstable best response but
is considerably more powerful in our game. The simulations further elucidate
the wide variety of asymmetric equilibria and demonstrate topological
consequences of the dynamics e.g. heavy-tailed degree distributions. Finally,
we report on a behavioral experiment on our game with over 100 participants,
where despite the complexity of the game, the resulting network was
surprisingly close to equilibrium.Comment: The short version of this paper appears in the proceedings of WINE-1
Network Creation Games: Think Global - Act Local
We investigate a non-cooperative game-theoretic model for the formation of
communication networks by selfish agents. Each agent aims for a central
position at minimum cost for creating edges. In particular, the general model
(Fabrikant et al., PODC'03) became popular for studying the structure of the
Internet or social networks. Despite its significance, locality in this game
was first studied only recently (Bil\`o et al., SPAA'14), where a worst case
locality model was presented, which came with a high efficiency loss in terms
of quality of equilibria. Our main contribution is a new and more optimistic
view on locality: agents are limited in their knowledge and actions to their
local view ranges, but can probe different strategies and finally choose the
best. We study the influence of our locality notion on the hardness of
computing best responses, convergence to equilibria, and quality of equilibria.
Moreover, we compare the strength of local versus non-local strategy-changes.
Our results address the gap between the original model and the worst case
locality variant. On the bright side, our efficiency results are in line with
observations from the original model, yet we have a non-constant lower bound on
the price of anarchy.Comment: An extended abstract of this paper has been accepted for publication
in the proceedings of the 40th International Conference on Mathematical
Foundations on Computer Scienc
Geometric Network Creation Games
Network Creation Games are a well-known approach for explaining and analyzing
the structure, quality and dynamics of real-world networks like the Internet
and other infrastructure networks which evolved via the interaction of selfish
agents without a central authority. In these games selfish agents which
correspond to nodes in a network strategically buy incident edges to improve
their centrality. However, past research on these games has only considered the
creation of networks with unit-weight edges. In practice, e.g. when
constructing a fiber-optic network, the choice of which nodes to connect and
also the induced price for a link crucially depends on the distance between the
involved nodes and such settings can be modeled via edge-weighted graphs. We
incorporate arbitrary edge weights by generalizing the well-known model by
Fabrikant et al.[PODC'03] to edge-weighted host graphs and focus on the
geometric setting where the weights are induced by the distances in some metric
space. In stark contrast to the state-of-the-art for the unit-weight version,
where the Price of Anarchy is conjectured to be constant and where resolving
this is a major open problem, we prove a tight non-constant bound on the Price
of Anarchy for the metric version and a slightly weaker upper bound for the
non-metric case. Moreover, we analyze the existence of equilibria, the
computational hardness and the game dynamics for several natural metrics. The
model we propose can be seen as the game-theoretic analogue of a variant of the
classical Network Design Problem. Thus, low-cost equilibria of our game
correspond to decentralized and stable approximations of the optimum network
design.Comment: Accepted at 31st ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA '19). 33 pages, 11 figure
Greedy Selfish Network Creation
We introduce and analyze greedy equilibria (GE) for the well-known model of
selfish network creation by Fabrikant et al.[PODC'03]. GE are interesting for
two reasons: (1) they model outcomes found by agents which prefer smooth
adaptations over radical strategy-changes, (2) GE are outcomes found by agents
which do not have enough computational resources to play optimally. In the
model of Fabrikant et al. agents correspond to Internet Service Providers which
buy network links to improve their quality of network usage. It is known that
computing a best response in this model is NP-hard. Hence, poly-time agents are
likely not to play optimally. But how good are networks created by such agents?
We answer this question for very simple agents. Quite surprisingly, naive
greedy play suffices to create remarkably stable networks. Specifically, we
show that in the SUM version, where agents attempt to minimize their average
distance to all other agents, GE capture Nash equilibria (NE) on trees and that
any GE is in 3-approximate NE on general networks. For the latter we also
provide a lower bound of 3/2 on the approximation ratio. For the MAX version,
where agents attempt to minimize their maximum distance, we show that any
GE-star is in 2-approximate NE and any GE-tree having larger diameter is in
6/5-approximate NE. Both bounds are tight. We contrast these positive results
by providing a linear lower bound on the approximation ratio for the MAX
version on general networks in GE. This result implies a locality gap of
for the metric min-max facility location problem, where n is the
number of clients.Comment: 28 pages, 8 figures. An extended abstract of this work was accepted
at WINE'1
Patterns and drivers of climatic niche dynamics during biological invasions of island-endemic amphibians, reptiles, and birds
Shifts between native and alien climatic niches pose a major challenge for predicting biological invasions. This is particularly true for insular species because geophysical barriers could constrain the realization of their fundamental niches, which may lead to underestimates of their invasion potential. To investigate this idea, we estimated the frequency of shifts between native and alien climatic niches and the magnitude of climatic mismatches using 80,148 alien occurrences of 46 endemic insular amphibian, reptile, and bird species. Then, we assessed the influence of nine potential predictors on climatic mismatches across taxa, based on species' characteristics, native range physical characteristics, and alien range properties. We found that climatic mismatch is common during invasions of endemic insular birds and reptiles: 78.3% and 55.1% of their respective alien records occurred outside of the environmental space of species' native climatic niche. In comparison, climatic mismatch was evident for only 16.2% of the amphibian invasions analyzed. Several predictors significantly explained climatic mismatch, and these varied among taxonomic groups. For amphibians, only native range size was associated with climatic mismatch. For reptiles, the magnitude of climatic mismatch was higher for species with narrow native altitudinal ranges, occurring in topographically complex or less remote islands, as well as for species with larger distances between their native and alien ranges. For birds, climatic mismatch was significantly larger for invasions on continents with higher phylogenetic diversity of the recipient community, and when the invader was more evolutionarily distinct. Our findings highlight that apparently common niche shifts of insular species may jeopardize our ability to forecast their potential invasions using correlative methods based on climatic variables. Also, we show which factors provide additional insights on the actual invasion potential of insular endemic amphibians, reptiles, and birds
Theory for the ultrafast ablation of graphite films
The physical mechanisms for damage formation in graphite films induced by
femtosecond laser pulses are analyzed using a microscopic electronic theory. We
describe the nonequilibrium dynamics of electrons and lattice by performing
molecular dynamics simulations on time-dependent potential energy surfaces. We
show that graphite has the unique property of exhibiting two distinct laser
induced structural instabilities. For high absorbed energies (> 3.3 eV/atom) we
find nonequilibrium melting followed by fast evaporation. For low intensities
above the damage threshold (> 2.0 eV/atom) ablation occurs via removal of
intact graphite sheets.Comment: 5 pages RevTeX, 3 PostScript figures, submitted to Phys. Re
High-harmonic generation from a confined atom
The order of high harmonics emitted by an atom in an intense laser field is
limited by the so-called cutoff frequency. Solving the time-dependent
Schr\"odinger equation, we show that this frequency can be increased
considerably by a parabolic confining potential, if the confinement parameters
are suitably chosen.
Furthermore, due to confinement, the radiation intensity remains high
throughout the extended emission range. All features observed can be explained
with classical arguments.Comment: 4 pages(tex files), 4 figures(eps files); added references and
comment
Relativistic treatment of harmonics from impurity systems in quantum wires
Within a one particle approximation of the Dirac equation we investigate a
defect system in a quantum wire. We demonstrate that by minimally coupling a
laser field of frequency omega to such an impurity system, one may generate
harmonics of multiples of the driving frequency. In a multiple defect system
one may employ the distance between the defects in order to tune the cut-off
frequency.Comment: 9 pages Latex, 8 eps figures, section added, numerics improve
Enhancement of bichromatic high-harmonic generation with a high-frequency field
Using a high-frequency field superposed to a linearly polarized bichromatic
laser field composed by a wave with frequency and a wave with
frequency , we show it is possible to enhance the intensity of a
group of high harmonics in orders of magnitude. These harmonics have
frequencies about 30% higher than the monochromatic-cutoff frequency, and,
within the three-step-model framework, correspond to a set of electron
trajectories for which tunneling ionization is strongly suppressed. Particular
features in the observed enhancement suggest that the high-frequency field
provides an additional mechanism for the electron to reach the continuum. This
interpretation is supported by a time-frequency analysis of the harmonic yield.
The additional high frequency field permits the control of this group of
harmonics leaving all other sets of harmonics practically unchanged, which is
an advantage over schemes involving only bichromatic fields.Comment: 6 pages RevTex, 5 figures (ps files), Changes in text, figures,
references and equations include
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