A new approach to the rent-partitioning problem in which players can submit bids over rooms. This differs from my Sperner's lemma approach in that here we assume that player preferences are linear over money, so that we can use a bidding model. This yields a finite procedure for obtaining a Pareto-efficient, envy-free division of the rent.

More generally, it applies to any fair division problem with indivisible goods and the possibility of monetary side payments. Moreover, the number of objects and players can be different. The procedure eliminates envy by compensating envious players. It is fully descriptive and says explicitly which compensations should be made, and in what order. Moreover, it is simple enough to be carried out without computer support.

We formally characterize the properties of the procedure, show how it establishes envy-freenes with minimal resources, and demonstrate its application to a wide class of fair-division problems.