1,620 research outputs found
Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case
This article is devoted to various methods (optimal transport, fixed-point,
ordinary differential equations) to obtain existence and/or uniqueness of
Cournot-Nash equilibria for games with a continuum of players with both
attractive and repulsive effects. We mainly address separable situations but
for which the game does not have a potential. We also present several numerical
simulations which illustrate the applicability of our approach to compute
Cournot-Nash equilibria
From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem
The notion of Nash equilibria plays a key role in the analysis of strategic
interactions in the framework of player games. Analysis of Nash equilibria
is however a complex issue when the number of players is large. In this article
we emphasize the role of optimal transport theory in: 1) the passage from Nash
to Cournot-Nash equilibria as the number of players tends to infinity, 2) the
analysis of Cournot-Nash equilibria
Egomunities, Exploring Socially Cohesive Person-based Communities
In the last few years, there has been a great interest in detecting
overlapping communities in complex networks, which is understood as dense
groups of nodes featuring a low outbound density. To date, most methods used to
compute such communities stem from the field of disjoint community detection by
either extending the concept of modularity to an overlapping context or by
attempting to decompose the whole set of nodes into several possibly
overlapping subsets. In this report we take an orthogonal approach by
introducing a metric, the cohesion, rooted in sociological considerations. The
cohesion quantifies the community-ness of one given set of nodes, based on the
notions of triangles - triplets of connected nodes - and weak ties, instead of
the classical view using only edge density. A set of nodes has a high cohesion
if it features a high density of triangles and intersects few triangles with
the rest of the network. As such, we introduce a numerical characterization of
communities: sets of nodes featuring a high cohesion. We then present a new
approach to the problem of overlapping communities by introducing the concept
of ego-munities, which are subjective communities centered around a given node,
specifically inside its neighborhood. We build upon the cohesion to construct a
heuristic algorithm which outputs a node's ego-munities by attempting to
maximize their cohesion. We illustrate the pertinence of our method with a
detailed description of one person's ego-munities among Facebook friends. We
finally conclude by describing promising applications of ego-munities such as
information inference and interest recommendations, and present a possible
extension to cohesion in the case of weighted networks
Triangles to Capture Social Cohesion
Although community detection has drawn tremendous amount of attention across
the sciences in the past decades, no formal consensus has been reached on the
very nature of what qualifies a community as such. In this article we take an
orthogonal approach by introducing a novel point of view to the problem of
overlapping communities. Instead of quantifying the quality of a set of
communities, we choose to focus on the intrinsic community-ness of one given
set of nodes. To do so, we propose a general metric on graphs, the cohesion,
based on counting triangles and inspired by well established sociological
considerations. The model has been validated through a large-scale online
experiment called Fellows in which users were able to compute their social
groups on Face- book and rate the quality of the obtained groups. By observing
those ratings in relation to the cohesion we assess that the cohesion is a
strong indicator of users subjective perception of the community-ness of a set
of people
Non-Uniform Time Sampling for Multiple-Frequency Harmonic Balance Computations
A time-domain harmonic balance method for the analysis of almost-periodic (multi-harmonics) flows is presented. This method relies on Fourier analysis to derive an efficient alternative to classical time marching schemes for such flows. It has recently received significant attention, especially in the turbomachinery field where the flow spectrum is essentially a combination of the blade passing frequencies. Up to now, harmonic balance methods have used a uniform time sampling of the period of interest, but in the case of several frequencies, non-necessarily multiple of each other, harmonic balance methods can face stability issues due to a bad condition number of the Fourier operator. Two algorithms are derived to find a non-uniform time sampling in order to minimize this condition number. Their behavior is studied on a wide range of frequencies, and a model problem of a 1D flow with pulsating outlet pressure, which enables to prove their efficiency. Finally, the flow in a multi-stage axial compressor is analyzed with different frequency sets. It demonstrates the stability and robustness of the present non-uniform harmonic balance method regardless of the frequency set
Biais dans les mesures obtenues par un réseau de capteurs sans fil
International audienceIn the area of complex networks, research has been stimulated by the availability of important data sets obtained through automatic measurement. In this article, we focus on interaction data in a hospital, gathered through the use of a wireless sensor network. We highlight the bias introduced by the measurement system and propose a method to reconstruct the original signal which evidences phenomenon which were not visible on the raw data
Optimal Transport and Cournot-Nash Equilibria
We study a class of games with a continuum of players for which
Cournot-Nash equilibria can be obtained by the minimisation of some cost,
related to optimal transport. This cost is not convex in the usual sense in
general but it turns out to have hidden strict convexity properties in many
relevant cases. This enables us to obtain new uniqueness results and a characterisation
of equilibria in terms of some partial differential equations, a simple
numerical scheme in dimension one as well as an analysis of the inefficiency of
equilibria
Optimal Transport and Cournot-Nash Equilibria
We study a class of games with a continuum of players for which
Cournot-Nash equilibria can be obtained by the minimisation of some cost,
related to optimal transport. This cost is not convex in the usual sense in
general but it turns out to have hidden strict convexity properties in many
relevant cases. This enables us to obtain new uniqueness results and a characterisation
of equilibria in terms of some partial differential equations, a simple
numerical scheme in dimension one as well as an analysis of the inefficiency of
equilibria
From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem
The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of N player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article we emphasize the role of optimal transport theory in: 1) the passage from Nash to Cournot-Nash equilibria as the number of players tends to infinity, 2) the analysis of Cournot-Nash equilibria
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