Asymmetrically fair rules for an indivisible good problem with a budget constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.