Optimal Allocation without Transfer Payments

Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known differences is not a viable option. In this paper, we find an optimal mechanism to allocate goods when the designer is benevolent. While the designer cannot charge agents, he can receive a costly but wasteful signal from them. We find conditions for which ignoring these costly signals by giving agents equal share (or using lotteries if the goods are indivisible) is optimal. In other cases, those that send the highest signal should receive the goods; however, we then show that there exist cases where more complicated mechanisms are superior. Finally, we show that the optimal mechanism is independent of the scarcity of the goods being allocated.