21 research outputs found
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
Optimal transport and Cournot-Nash equilibria
International audienceWe 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
On the Jordan-Kinderlehrer-Otto scheme
In this paper, we prove that the Jordan-Kinderlehrer-Otto scheme for a family
of linear parabolic equations on the flat torus converges uniformly in space.Comment: 15 page
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
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
Dealing with moment measures via entropy and optimal transport
A recent paper by Cordero-Erausquin and Klartag provides a characterization
of the measures on which can be expressed as the moment measures
of suitable convex functions , i.e. are of the form (\nabla u)\_\\#e^{- u}
for and finds the corresponding by a
variational method in the class of convex functions. Here we propose a purely
optimal-transport-based method to retrieve the same result. The variational
problem becomes the minimization of an entropy and a transport cost among
densities and the optimizer turns out to be . This
requires to develop some estimates and some semicontinuity results for the
corresponding functionals which are natural in optimal transport. The notion of
displacement convexity plays a crucial role in the characterization and
uniqueness of the minimizers