  We study generalized games with full row rank equality constraints and we
provide a strikingly simple proof of strong monotonicity of the associated KKT
operator. This allows us to show linear convergence to a variational
equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we
propose a fully-distributed algorithm with linear convergence guarantee for
aggregative games under partial-decision information. Based on these results,
we establish stability properties for online GNE seeking in games with
time-varying cost functions and constraints. Finally, we illustrate our
findings numerically on an economic dispatch problem for peer-to-peer energy
markets.
