  We address the generalized Nash equilibrium seeking problem for a population
of agents playing aggregative games with affine coupling constraints. We focus
on semi-decentralized communication architectures, where there is a central
coordinator able to gather and broadcast signals of aggregative nature to the
agents. By exploiting the framework of monotone operator theory and operator
splitting, we first critically review the most relevant available algorithms
and then design two novel schemes: (i) a single-layer, fixed-step algorithm
with convergence guarantee for general (non cocoercive, non-strictly) monotone
aggregative games and (ii) a single-layer proximal-type algorithm for a class
of monotone aggregative games with linearly coupled cost functions. We also
design novel accelerated variants of the algorithms via (alternating) inertial
and over-relaxation steps. Finally, we show via numerical simulations that the
proposed algorithms outperform those in the literature in terms of convergence
speed.
