On public good provision mechanisms with dominant strategies and balanced budget

Consider a mechanism for the binary public good provision problem that is dominant strategy incentive compatible (DSIC), ex-post individually rational (EPIR), and ex-post budget balanced (EPBB). Suppose this mechanism has the additional property that the utility from participating in the mechanism to the lowest types is zero for all agents. Such a mechanism must be of a threshold form, in which there is a fixed threshold for each agent such that the public good is not provided if there is an agent with a value below her threshold and is provided if all agents' values exceed their respective threshold. There are mechanism that are DSIC, EPIR, and EPBB that are not of the threshold form. Mechanisms that maximize welfare subject to DSIC, EPIR, and EPBB must again have the threshold form. Finally, mechanisms that are DSIC, EPIR, EPBB and that furthermore satisfy the condition that there is at least one type profile in which all agents can block the provision of the public good, also must be of the threshold form. As we allow individuals' values for the public good to be negative and positive, our results cover examples including bilateral trade, bilateral wage negotiations, a seller selling to a group of individuals (who then have joint ownership rights), and rezoning the use of land.