Dilemma concerning street musicians/beggars?

A strange, be it minor, dilemma I have.
When I was in Athens some weeks ago I was drinking a beer with my girlfriend and some friends, down of the Parthenon.
In the streets there are quite some beggars, immigrants who sell all kind of stuff and street musicians.
Every now and then I buy a lighter or some paper handkerchiefs.
I’m happy, they’re happy.
And sometimes a musician comes to your table and plays a bit.
Now here’s the dilemma: If you give some money (which is what they want) because you like their music, they disappear.
If you don’t give, they will stay and keep on playing (until you give some anyway, after some time).
So what gives?
Give nothing and enjoy the music (but leaving the musician annoyed and yourself with a feeling of awkwardness) or give some money and see them take off (a few coins lighter and drinking your beer without accompanying music)?