Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nash-type equilibria on Riemannian manifolds: a variational approach   Motivated by Nash equilibrium problems on 'curved' strategy sets, the concept
of Nash-Stampacchia equilibrium points is introduced via variational
inequalities on Riemannian manifolds. Characterizations, existence, and
stability of Nash-Stampacchia equilibria are studied when the strategy sets are
compact/noncompact geodesic convex subsets of Hadamard manifoleds, exploiting
two well-known geometrical features of these spaces both involving the metric
projection map. These properties actually characterize the {non-positivity} of
the sectional curvature of complete and simply connected Riemannian spaces,
delimiting the Hadamard manifolds as the optimal geometrical framework of
Nash-Stampacchia equilibrium problems. Our analytical approach exploits various
elements from set-valued and variational analysis, dynamical systems, and
non-smooth calculus on Riemannian manifolds. Examples are presented on the
Poincar\'e upper-plane model and on the open convex cone of symmetric positive
definite matrices endowed with the trace-type Killing form.

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The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
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The categories of this paper are: cs
11
The categories of this paper are: hep-lat