  We present infrared K'- (2.1 micron) and L'-band (3.8 micron)
high-spatial-resolution (<0.3") imaging observations of 17 nearby (z < 0.17)
ultraluminous infrared galaxies (ULIRGs) assisted with the adaptive optics of
the Subaru Telescope. We search for compact red K'-L' color emission as the
indicator of luminous active galactic nuclei (AGNs) due to AGN-heated hot dust
emission. Two luminous dual AGN candidates are revealed. Combining these
results with those of our previous study, we can state that the detected
fraction of luminous dual AGNs in nearby ULIRGs is much less than unity (<20%),
even when infrared wavelengths >2 micron are used that should be sensitive to
buried AGNs due to small dust extinction effects. For ULIRGs with resolved
multiple nuclear K'-band emission, we estimate the activation of supermassive
black holes (SMBHs) at individual galaxy nuclei in the form of AGN luminosity
normalized by SMBH mass inferred from host galaxy stellar luminosity. We
confirm a trend that more massive SMBHs in K'-band brighter primary galaxy
nuclei are generally more active, with higher SMBH-mass-normalized AGN
luminosity than less massive SMBHs in K'-band fainter secondary galaxy nuclei,
as predicted by numerical simulations of gas-rich major galaxy mergers. In two
sources, the presence of even infrared elusive extremely deeply buried AGNs is
indicated by comparisons with available (sub)millimeter data. Non-synchronous
SMBH activation (i.e., less activation of less massive SMBHs) and the possible
presence of such infrared elusive AGNs may be responsible for the small
fraction of infrared-detected luminous dual AGNs in nearby merging ULIRGs.
