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We investigate the characteristic radiative efficiency \epsilon, Eddingtonratio \lambda, and duty cycle P_0 of high-redshift active galactic nuclei(AGN), drawing on measurements of the AGN luminosity function at z=3-6 and,especially, on recent measurements of quasar clustering at z=3-4.5 from theSloan Digital Sky Survey. The free parameters of our models are \epsilon,\lambda, and the normalization, scatter, and redshift evolution of the relationbetween black hole mass \mbh and halo virial velocity V_vir. We compute theluminosity function from the implied growth of the black hole mass function andthe quasar correlation length from the bias of the host halos. We test ouradopted formulae for the halo mass function and halo bias against measurementsfrom the large N-body simulation developed by the MICE collaboration. Thestrong clustering of AGNs observed at z=3 and, especially, at z=4 implies thatmassive black holes reside in rare, massive dark matter halos. Reproducing theobserved luminosity function then requires high efficiency \epsilon and/or lowEddington ratio \lambda, with a lower limit (based on 2\sigma agreement withthe measured z=4 correlation length) \epsilon> 0.7\lambda/(1+0.7\lambda),implying \epsilon > 0.17 for \lambda > 0.25. Successful models predict highduty cycles, P_0~0.2, 0.5, and 0.9 at z=3.1, 4.5 and 6, respectively, and theyrequire that the fraction of halo baryons locked in the central black hole ismuch larger than the locally observed value. The rapid drop in the abundance ofthe massive and rare host halos at z>7 implies a proportionally rapid declinein the number density of luminous quasars, much stronger than simpleextrapolations of the z=3-6 luminosity function would predict. (abridged)

On the radiative efficiencies, Eddington ratios, and duty cycles of luminous high-redshift quasars