The common practice of bypassing the indivisibility of objects with cash compensations has received little attention in the fair division literature, with the single exception of the assignment problem. Under general combinatorial utilities we compare two division rules with cognitively feasible and privacy preserving individual messages, much simpler than reporting the value of each subset of goods.
In Sell&Buy agents bid for the role of Seller or Buyer: with two agents the smallest bid defines the Seller who charges to the Buyer a price constrained only by her winning bid.
In Divide&Choose agents bid for the role of Divider, then everyone bids on the shares of the Dividerís partition.
Both rules offer strong Guarantees (worst case utilities) rewarding (resp. penalising) subadditive (resp. superadditive) utilities beyond the benchmark "fair share" of the bundled goods. Such guarantees are not compatible with an Envy-Free final allocation but allow for the alternative interpretation of ex post fairness as the Stand Alone Upper Bound. Playing safe in the S&B rule mostly implements the SAUB, which the D&C rule does not.
Playing safe in both rules is inefficient, often not much so, when all utilities are additive.
Playing safe is efficient with the D&C rule but not for the S&B rule when utilities are identical.
Playing safe is efficient with the S&B rule but not for the D&C rule when an agent's utility for the goods dominates the others'.
Paper available at http://arxiv.org/abs/2202.08117 [econ.TH]
Links to the seminar recording and the slides.