Who Pays for the Bridge

A town can build a bridge costing 90, paid for by an outside funder (the town's budget is not involved). Three citizens have private valuations of 50, 30 and 25 for the bridge. They each report a value and the town uses the Clarke pivot (VCG) mechanism: build the bridge if the reported total value exceeds its cost, so that total reported value minus cost is maximised; and charge each citizen the amount by which their presence lowers the best attainable (reported value minus cost) welfare of the *other two* citizens, relative to what the others get with the bridge-or-not decision actually made. Assume everyone reports truthfully. What is the sum of the three payments?

• dominant strategy

Source: Clarke pivot (VCG) mechanism for public goods (Vickrey 1961, Clarke 1971, Groves 1973); the valuations are invented for AxiomIQ. Statement written for AxiomIQ.