Martin Spann et al. have published "Pay What You Want as a Pricing Model for Open Access Publishing?" in Communications of the ACM.
Here's an excerpt:
The observed payments from our experiment together with the preliminary results from other experiments (that is, Cogent OA) indicate that PWYW may work in the context of open access publishing. The results suggest that a substantial fraction of authors do pay APCs voluntarily, in some cases even more than regularly asked.