Reassignment-proof rules for land rental problems

We consider land rental problems where there are several communities that can act as lessors and a single tenant who does not necessary need all the available land. A rule should determine which communities become lessors, how much land they rent and at which price. We present a complete characterization of the family of rules that satisfy reassignment-proofness by merging and spliting, apart from land monotonicity. We also define two parametric subfamilies. The first one is characterized by adding a property of weighted standard for two-person. The second one is characterized by adding consistency and continuity.