A copolymer that has sufficient dispersibility to various kinds of cements, including those having low fluidity (difficult cement). The copolymer is obtained by polymerizing monomer components including an unsaturated (poly)alkylene glycol ether monomer (a), an unsaturated carboxylic acid monomer (b), and an unsaturated cross-linkable monomer (c) or an unsaturated cross-linkable monomer (d). The unsaturated cross-linkable monomer (c) is allyl itaconate or allyl citraconate, or ester thereof. The unsaturated cross-linkable monomer (d) is an ester obtained by reaction of at least one acid, selected from the group consisting of (meth)acrylic acid, maleic acid, fumaric acid, itaconic acid, and citraconic acid and ester derived from the acids, with a (poly)alkylene glycol or a (poly)alkylene glycol ether.