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). It is well known that if there are only two agents, then any such mechanism must have a threshold (or fixed cost-sharing) form, providing the public good if and only if both agents have values that are at least their respective thresholds. When there are more than two agents, there are mechanisms that are DSIC, EPIR, and EPBB that are not of the threshold form. Any DSIC, EPIR, and EPBB mechanism that additionally satisfies that the lowest types expect zero net utility from participating are again of the threshold form. This additional condition arises endogenously when maximizing expected welfare subject to DSIC, EPIR, and EPBB.