Rules (of Bidding) to Generate Equal Stated Profits: An Axiomatic Approach

Although one may hope to achieve equality of stated profits without enforcing it, one may not trust in such voluntary equality seeking and rather try to impose rules (of bidding) guaranteeing it. Our axiomatic approach is based on envy-free net trades according to bids, which, together with the equality requirement, characterize the first-price auction and fair-division game.