  In the interaction of laser pulses of extreme intensity ($>10^{23}~{\rm W
cm}^{-2}$) with high-density, thick plasma targets, simulations show
significant radiation friction losses, in contrast to thin targets for which
such losses are negligible. We present an analytical calculation, based on
classical radiation friction modeling, of the conversion efficiency of the
laser energy into incoherent radiation in the case when a circularly polarized
pulse interacts with a thick plasma slab of overcritical initial density. By
accounting for three effects including the influence of radiation losses on the
single electron trajectory, the global `hole boring' motion of the laser-plasma
interaction region under the action of radiation pressure, and the
inhomogeneity of the laser field in both longitudinal and transverse direction,
we find a good agreement with the results of three-dimensional particle-in-cell
simulations. Overall, the collective effects greatly reduce radiation losses
with respect to electrons driven by the same laser pulse in vacuum, which also
shift the reliability of classical calculations up to higher intensities.
