Population monotonic and strategy-proof mechanisms respecting welfare lower bounds

The significance of population monotonicity and welfare bounds is well-recognized in the fair division literature. We consider the welfare bounds that are central to the fair allocation literature, namely, the identical-preferences lower-bound, individual rationality, the stand-alone lower-bound,   and k$k$-fairness. We characterize population monotonic and incentive compatible mechanisms which allocate an object efficiently and respect a welfare lower bound chosen in the fair allocation problem of allocating a collectively owned indivisible good or bad when monetary transfers are possible and preferences are private information.