  We investigate the sensitivity of the Nash equilibrium of constrained network
aggregative games to changes in exogenous parameters affecting the cost
function of the players. This setting is motivated by two applications. The
first is the analysis of interventions by a social planner with a networked
objective function while the second is network routing games with atomic
players and information constraints. By exploiting a primal reformulation of a
sensitivity analysis result for variational inequalities, we provide a
characterization of the sensitivity of the Nash equilibrium that depends on
primal variables only. To derive this result we assume strong monotonicity of
the mapping associated with the game. As the second main result, we derive
sufficient conditions that guarantee this strong monotonicity property in
network aggregative games. These two characterizations allows us to
systematically study changes in the Nash equilibrium due to perturbations or
parameter variations in the two applications mentioned above.
