Exact Budget Balance via Payment-Rule Ambiguity: Incentive Preservation, Transfer Capacity, and Participation

This paper asks whether the payment side of an incentive-compatible mechanism can be repaired so that every realized settlement balances exactly while the allocation and all report-by-report comparisons under the maintained worst-case evaluation remain unchanged. Before reports, the designer commits to a menu of payment rules and a report-blind selection protocol. A pointwise preservation condition then carries over dominant-strategy incentives. Under a full-support common reference, a precisely known label law permits repair only if the original rule already balances, whereas frequency uncertainty about even one non-worst label makes every non-deficit rule repairable. Under the common residual-ambiguity benchmark, every preserving, exactly balanced finite menu at a positive-surplus state requires more transfer capacity as certified frequency information becomes tighter. In the canonical menu, fixing the transfer cap makes the best attainable balance deteriorate toward the original surplus as ambiguity vanishes. When only the possible labels are certified, two labels suffice. Suitably balanced partitions can also retain the original cap for nonnegative payments and preserve individual rationality under every realized rule. This last guarantee is impossible in positive-revenue Vickrey states when each agent's preserving distribution has full support. Frequency information therefore changes feasibility, liquidity, and realized participation in distinct ways.