most inks, like paints, consist of a pigment, a polymer binder in a solvent or dispersed in water with coalescing solvents, some dispersing aids and surfactants and usually some inert fillers.
If you want an ink that is water wipeable then you will need to have a water soluble poymer binder and maybe a water soluble pigment too - although the binder is what holds it all together, so if you have a binder that is water soluble then it figures that wioping the dry coating/ink with a wet cloth will get the polymer to dissolve and you should be able to wipe it off.
Hope that helps - google paint or ink formulations for some standard formulations, but as I said, they are all:
1) Pigment
2)Binder
3)solvent or water
4)surfactants/dispersing aids
5)fillers
P