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.

► Study the allocation of identical items that are complements to bidders with budgets. ► Show that no deterministic mechanism simultaneously satisfies four desirable properties. ► Two properties are strategic: individual-rationality and strategy-proofness. ► Two properties are normative: Pareto-efficiency and no-positive-transfers. ► True even for two bidders, two items, and public budgets; extends to richer domains.