What money canʼt buy: Efficient mechanism design with costly signals

► A set of heterogeneous objects is allocated to a set of ex-ante heterogeneous agents. ► There is no money. Private values indicate willingness to engage in costly signaling. ► The designer faces a trade-off between allocative efficiency and cost minimization. ► The set of ex-ante Pareto efficient allocation mechanisms is characterized. ► Practical implementation via all-pay auctions is proposed.