All of the answers didn't work for me, I checked the playlist URL and seen that playlist parameter changed to list! So it should be:
&loop=1&list=PLvNxGp1V1dOwpDBl7L3AJIlkKYdNDKUEs
So here is the full code I use make a clean, looping, autoplay video:
<iframe width="100%" height="425" src="https://www.youtube.com/embed/MavEpJETfgI?autoplay=1&showinfo=0&loop=1&list=PLvNxGp1V1dOwpDBl7L3AJIlkKYdNDKUEs&rel=0" frameborder="0" allowfullscreen></iframe>