A polymer of the formula (I): ##STR1## in which X.sub.1 means H or (R.sub.1).sub.1+1 --L.sub.1 CO--, X.sub.2 means --(L.sub.2).sub.m --OH or ##STR2## R.sub.1 means --COO.sup.- M.sup.+, --SO.sub.3.sup.- M.sup.+ or (M.sup.+).sub.2 PO.sub.3.sup.2-, L.sub.1 means alkylene, arylene, aralkylene or cycloalkylene, L.sub.2 means the residue of a polyether having an average molecular weight of 200 to 3000 (number average), M.sup.+ means a cation, l means a number from 0 to 4, m means a number 0 or 1 and n means a number from 0 to 20, wherein m+n is .gtoreq.1.
An additive for a rubber composition consists essentially of an ester of (i) an aliphatic polyvalent carboxylic acid with (iii) a (poly)oxyalkylene derivative, and having at least one carboxyl group in its molecule, or an ester of (ii) an aromatic polyvalent carboxylic acid with (iii) a (poly)oxyalkylene derivative, and having at least one carboxyl group bonded to an aromatic ring in its molecule. And also, it relates to an additive composition, a rubber composition and a pneumatic tire using such an additive for a rubber composition.