Money Burning and Implementation

In response to public disapproval for any electronic mail system that includes a charge for sending email, computational spam fighting, which was originally proposed in (4), has reemerged as an economic approach that could be used to prevent spam in email systems (3). This approach requires email senders to solve a challenge that expends their computational resources but otherwise has no direct social benefit. This challenge is tantamount to requiring that the sender burn money. This paper explores the extent to which money burning may be useful in broader implementation contexts. We consider the general problem of designing socially optimal, single round, sealed bid mechanisms when transfers made from the agents to the mechanism must be burnt (i.e., are a social loss). In these settings the socially optimal outcome is the one that maximizes the marginal surplus, that is, the sum of the agents' valuations minus the agents' payments (minus any social cost of the outcome). In the Bayesian setting where the agents' valuations are drawn independently, but not necessarily identically, from a known distribution, we give a concise characterization of the mechanism that maximizes the expected marginal surplus. From this characterization we observe that the socially optimal way to allocate a single item to agents with i.i.d. valuations is, depending on the distribution, to either assign the item to an arbitrary agent or to run a second-price-like auction. Furthermore, for non-identical distributions that satisfy the monotone hazard rate condition, the socially optimal mechanism (for any given social cost function) is the one that chooses the allocation to maximize the expected social surplus ex ante and requires no payments.