A composition containing
metal based nanoparticles (X), a
polymer (Y), and a dispersion medium, the
polymer (Y) being a
vinyl polymer having a chain-like
alkyl group having 10 to 28 carbon atoms and a
nitrogen-containing heterocyclic group, the
metal based nanoparticles (X) and the
polymer (Y) being dispersed in the dispersion medium, the composition being used as an additive composition for a lubricating oil composition, an additive composition for a
grease composition, a lubricating oil composition, or a
grease composition. The polymer (Y) is one or more kind selected from the group consisting of a polymer (Y1) that contains two or more kinds selected from the group consisting of a constitutional unit derived from the following
monomer (ya), a constitutional unit derived from the following
monomer (yb), and a constitutional unit derived from the following
monomer (yc), and a polymer (Y2) that contains a constitutional unit derived from the following monomer (yb) and does not contain a constitutional unit derived from the following monomer (ya) and a constitutional unit derived from the following monomer (yc): monomer (ya): an olefin having 12 to 30 carbon atoms, monomer (yb): a vinyl monomer having a
nitrogen-containing heterocyclic group, at least one
hydrogen atom of which is substituted by a chain-like
alkyl group having 12 to 30 carbon atoms, and monomer (yc): a vinyl monomer having a
nitrogen-containing heterocyclic group, all
hydrogen atoms of which are not substituted by a chain-like
alkyl group having 12 to 30 carbon atoms.