I was curious about the theory behind a reverse auction system where some suppliers act in a non-profit manner, namely, that their consideration of extra-auctions benefits of providing their service results in a free offer to the buyer.
Can such a system exist where there are some suppliers willing to provide free services and others suppliers that are not willing to provide free services?
Is an equilibrium possible if, say, 30% of the potential suppliers acted in such a voluntary manner or would this result in a market failure?
Any guiding thoughts or material would be very welcomed.
Edit: Most of the literature I've read came from the internal references within this review: https://www.sciencedirect.com/science/article/abs/pii/S1366554503000711 (paywalled)
I also read about the auction rulesets defined in this work: https://web.stanford.edu/~milgrom/publishedarticles/Putting%20Auction%20Theory%20to%20Work.pdf
Neither of the above references, to my knowledge, accounted for the consequences of non-profit reverse auction bids.