  In this letter, we study distributed optimization and Nash
equilibrium-seeking dynamics from a contraction theoretic perspective. Our
first result is a novel bound on the logarithmic norm of saddle matrices.
Second, for distributed gradient flows based upon incidence and Laplacian
constraints over arbitrary topologies, we establish strong contractivity over
an appropriate invariant vector subspace. Third, we give sufficient conditions
for strong contractivity in pseudogradient and best response games with
complete information, show the equivalence of these conditions, and consider
the special case of aggregative games.
