  In this paper, we extend a recently introduced multi-fidelity control variate
for the uncertainty quantification of the Boltzmann equation to the case of
kinetic models arising in the study of multiagent systems. For these phenomena,
where the effect of uncertainties is particularly evident, several models have
been developed whose equilibrium states are typically unknown. In particular,
we aim to develop efficient numerical methods based on solving the kinetic
equations in the phase space by Direct Simulation Monte Carlo (DSMC) coupled to
a Monte Carlo sampling in the random space. To this end, exploiting the
knowledge of the corresponding mean-field approximation we develop novel
mean-field Control Variate (MFCV) methods that are able to strongly reduce the
variance of the standard Monte Carlo sampling method in the random space. We
verify these observations with several numerical examples based on classical
models , including wealth exchanges and opinion formation model for collective
phenomena.
