We study the problem of how to allocate in identical items among n > m agents, assuming each agent desires exactly one item and has a private value for consuming it. We assume the items are jointly owned by the agents, not by one uninformed center, so an auction cannot be used to solve our problem. Instead, the agents who receive items compensate those who do not. This problem has been studied by others recently, and their solutions have modified the classic VCG mechanism. This approach guarantees strategy-proofness and allocative efficiency. Further, in an auction setting, VCG guarantees budget balance, because payments are absorbed by the auctioneer. In our setting, however, where payments are redistributed to the agents, some money must be burned in order to retain strategy-proofness. While strategy-proofness is necessary for truthful implementation, allocative efficiency (allocating the m items to those that desire them most), is not always an appropriate goal in our setting. Rather, we contend that maximizing social surplus is. In service of this goal, we study a class of mechanisms that may burn not only money but destroy items as well. Our key finding is that destroying items can save money, and hence lead to greater social surplus. More specifically, our first observation is that a mechanism is strategy-proof iff it admits a threshold representation. Given this observation, we restrict attention to specific threshold and payment functions for which we can numerically solve for an optimal mechanism. Whereas the worst-case ratio of the realized social surplus to the maximum possible is close to 1 when m = 1 and 0 when m = n - 1 under the VCG mechanism, the best mechanism we find coincides with VCG when m = 1 but has a ratio approaching 1 when m = n - 1 as n increases.
