A note on the incompatibility of strategy-proofness and Pareto-optimality in quasi-linear settings with public budgets

We show that any deterministic mechanism, for allocating identical items that are complements to budget-constrained bidders, cannot simultaneously satisfy individual-rationality, strategy-proofness, Pareto-efficiency, and no-positive-transfers. This holds even for two bidders, two items, and commonly-known budgets, and generalizes to richer settings.