The idealized garb of philosophers among the Greeks was taken from the symbols of Cynicism: a cloak to keep off the elements, a bag or purse to hold all of one's worldly possessions, and a staff for walking. The staff and purse are shown on the Boscoreale treasure's philosophy cup. No cloak was necessary here--all of the figures on the cup are skeletons, underlining the link between philosophy and death.
But Epicurus was not a Cynic. He also didn't hold forth publicly in the regimented world of the gymnasiarchs. Presumably he wore what was handy, some of it purchased and some, perhaps, gifted.
Plato's Academy mosaic - Wikipedia
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This mosaic from Herculaneum is thought to depict Greek philosophers as Romans would have imagined them.
