"Non-linear transfer function" is a generalization of "quadratic payments." "Transfer function" is a general engineering term meaning a mathematical description of the output of a system in terms of its inputs. So the "transfer function" of a payment is its output (what you get) in terms of its input (what you pay). Normally that transfer function is linear: if one apple costs a dollar, then N apples will cost N dollars. (Actually, that's only true up to a point. In the real world, if N is large enough, N apples will cost you less than $N.)