  We calculate the relation between the bare coupling constant g_0 and the
MSbar-renormalized coupling g_MS: g_0 = Z_g(g_0,a \mu) g_MS, to 2 loops in
perturbation theory. We employ the standard Wilson action for gluons and the
overlap action for fermions. For convenience, we have worked with the
background field technique, which only requires evaluation of 2-point Green's
function for the problem at hand. Our results depend explicitly on the number
of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the
overlap parameter rho cannot be extracted analytically, we tabulate our results
for different values in the allowed range of rho (0 < rho < 2), focusing on
values which are being used most frequently in simulations. Knowledge of Z_g
allows us to derive the 3-loop coefficient of the bare beta-function
(beta_L(g_0)) which, unlike the 1- and 2-loop coefficients, is
regularization-dependent. The nontrivial dependence of Z_g and of beta_L(g_0)
on rho is plotted for various choices of N, N_f.
