cluster galaxies are drawn from the same distribution; then we take a simple model for cannibalism, by merging two of the galaxies (the brightest plus one other) in the first example. Finally, in section 7 we present the results of all models for the average magnitude of first and second brightest galaxies as well the dispersion of the former as a function of cluster luminosity. We then compare these results with observations.

Throughout we have used a concordance cosmological model, with $\Omega_m=0.24$, $\Omega_\Lambda=0.76$, $h=0.735$ and $\sigma_8=0.74$ [@wmap].

The Mass-luminosity relation
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The work presented below is based on the non-parametric model for relating galaxy luminosity with halo/subhalo mass presented in paper I. The basic idea is that more massive haloes/subhaloes have deeper potential wells and will thus accrete more gas and subsequently will have more luminous galaxies forming within them. In effect, we take the relation between galaxy luminosity and halo/subhalo mass to be one to one and monotonic. An additional extra ingredient is necessary to maintain this approximation in the framework of the model, since subhaloes lose mass to the parent halo after accretion due to tidal interactions. Alternatively put, a halo is not simply the sum of the 