Don't use any solvents on plexiglass. It always helps to know what NOT to use
Alcohol is a solvent even if rubbing alcohol is a diluted with water form of it. Depending on what they used for a marker you could end up driving the stain deeper into the plastic instead of removing it all. So do not use alcohol, it would work great on glass but not on plastic.
If they used a dye marker that was solvent based then the die might have penetrated into the surface in which case you will be well frustrated in any attempt to get rid of it. Lets hope it is just a bit of surface residue.
Do a search on Novus plastic polish kit
If that does not do it then you have a choice of going with micron flexible grit polishing papers from 3M
. You can work your way through those using finer and finer grits and then finish the job with the Novus plastic polish kit. The link to the micron papers is from a guitar makers site. I used that site because they have good prices and are reputable sellers. Other people sell this specialty polishing paper as well.