Strategy-proof mechanisms in public good economies

In economies with one private good and one public good, the minimal provision mechanism is shown to be the unique mechanism that satisfies strategy-proofness, voluntary participation and the full-range property when a given cost share rule has the convex property. Even if the cost share rule shares positive fixed costs of producing public goods, so includes a non-convex portion, the proper restriction of the range of mechanisms guarantees that the minimal provision mechanism satisfies strategy-proofness and voluntary participation. In contrast, if the restriction is not sufficient, then the implied non-convexity of the cost share rule leads to an impossibility result. Furthermore, we show that no satisfactory mechanism exists in the case with several public goods.