it seems like in the event that quadratic payments are applied to a situation where multiple parties are competing for a single good that it reduces to something similar to an auction. Imo it's clear that auctions, corresponding with what you said, favor those with the most income.
Yes, and adding a non-linear transfer function won't help in this case. To win an auction, I only need to outbid you by epsilon. Non-linear payments only help where the value of the thing being purchased can vary (non-linearly) with the purchase price.
can you go into more detail on this? it sounds interesting. What's an example of somethings value that varies non-linearly with the purchase price? Is a "non-linear transfer function" a stand-in for "quadratic payments" in this case?
"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.)
