That’s neat, I’d never heard of it before!

It is an open question whether an Angel of some power k can escape forever.

Looks like you’re quoting the Proceedings of 11th Annual International Conference on Computing and Combinatorics from 2005: dl.acm.org/doi/abs/10.5555/2958119.2958180

Apparently, it was solved (twice!) the next year.

In late 2006, the original problem was solved when independent proofs appeared, showing that an angel can win. Bowditch proved that a 4-angel (that is, an angel with power k = 4) can win[2] and Máthé[3] and Kloster[4] gave proofs that a 2-angel can win.

en.wikipedia.org/wiki/Angel_problem