I had to do a little investigation to find an answer to your great question. A lot of websites claim pump hairspray works great for ink stains. The main ingredient for pump hairsprays is alcohol. It is not the active ingredient, i.e. the stuff that sticks hair strands together (see this website for various active ingredients in hairspray)

Instead, alcohol is the solvent in which the active ingredients are dissolved. In fact, alcohol is a common solvent because it's good at dissolving things due to it's chemical structure. Alcohol has a polar group (an oxygen and hydrogen) and what's called an alkyl group (three hydrogens bound to a carbon). Most inks also have both alkyl groups and polar groups, too. When two chemicals have similar chemical structures (like ink and alcohol), they mix together well, which is another way of saying one easily dissolves the other. When getting an ink stain out, the alcohol dissolves the ink off of fabric, your skin, or a tabletop allowing you to easily wash it off. Since both ink and alcohol have polar groups, they also can dissolve well in water, which, as you know, is comprised of two hydrogens and an oxygen. So alcohol can be used to easily remove ink stains because of their chemical similarity to each other.

Another tip: nail polish remover can be used to remove about any ink stain you can imagine. It's chemical structure is found in many organic compounds (ink, oil, and nail polish are all organic compounds) so it's able to easily dissolve them all. Find out what the main ingredient of nail polish is here: