  This is the second installment in a series of papers aimed at generalizing
symplectic capacities and homologies. We study symmetric versions of symplectic
capacities for real symplectic manifolds, and obtain corresponding results for
them to those of the first [19] of this series (such as representation formula,
a theorem by Evgeni Neduv, Brunn-Minkowski type inequality and Minkowski
billiard trajectories proposed by Artstein-Avidan-Ostrover).
