114 research outputs found
Optimal Budget Allocation in Social Networks: Quality or Seeding
In this paper, we study a strategic model of marketing and product
consumption in social networks. We consider two competing firms in a market
providing two substitutable products with preset qualities. Agents choose their
consumptions following a myopic best response dynamics which results in a
local, linear update for the consumptions. At some point in time, firms receive
a limited budget which they can use to trigger a larger consumption of their
products in the network. Firms have to decide between marginally improving the
quality of their products and giving free offers to a chosen set of agents in
the network in order to better facilitate spreading their products. We derive a
simple threshold rule for the optimal allocation of the budget and describe the
resulting Nash equilibrium. It is shown that the optimal allocation of the
budget depends on the entire distribution of centralities in the network,
quality of products and the model parameters. In particular, we show that in a
graph with a higher number of agents with centralities above a certain
threshold, firms spend more budget on seeding in the optimal allocation.
Furthermore, if seeding budget is nonzero for a balanced graph, it will also be
nonzero for any other graph, and if seeding budget is zero for a star graph, it
will be zero for any other graph too. We also show that firms allocate more
budget to quality improvement when their qualities are close, in order to
distance themselves from the rival firm. However, as the gap between qualities
widens, competition in qualities becomes less effective and firms spend more
budget on seeding.Comment: 7 page
On stochastic imitation dynamics in large-scale networks
We consider a broad class of stochastic imitation dynamics over networks,
encompassing several well known learning models such as the replicator
dynamics. In the considered models, players have no global information about
the game structure: they only know their own current utility and the one of
neighbor players contacted through pairwise interactions in a network. In
response to this information, players update their state according to some
stochastic rules. For potential population games and complete interaction
networks, we prove convergence and long-lasting permanence close to the
evolutionary stable strategies of the game. These results refine and extend the
ones known for deterministic imitation dynamics as they account for new
emerging behaviors including meta-stability of the equilibria. Finally, we
discuss extensions of our results beyond the fully mixed case, studying
imitation dynamics where agents interact on complex communication networks.Comment: Extended version of conference paper accepted at ECC 201
Feature Extraction from Degree Distribution for Comparison and Analysis of Complex Networks
The degree distribution is an important characteristic of complex networks.
In many data analysis applications, the networks should be represented as
fixed-length feature vectors and therefore the feature extraction from the
degree distribution is a necessary step. Moreover, many applications need a
similarity function for comparison of complex networks based on their degree
distributions. Such a similarity measure has many applications including
classification and clustering of network instances, evaluation of network
sampling methods, anomaly detection, and study of epidemic dynamics. The
existing methods are unable to effectively capture the similarity of degree
distributions, particularly when the corresponding networks have different
sizes. Based on our observations about the structure of the degree
distributions in networks over time, we propose a feature extraction and a
similarity function for the degree distributions in complex networks. We
propose to calculate the feature values based on the mean and standard
deviation of the node degrees in order to decrease the effect of the network
size on the extracted features. The proposed method is evaluated using
different artificial and real network datasets, and it outperforms the state of
the art methods with respect to the accuracy of the distance function and the
effectiveness of the extracted features.Comment: arXiv admin note: substantial text overlap with arXiv:1307.362
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
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