On collective goods, private wealth, and the core solution of simple games with sidepayments

Abstract

This essay identifies consequences for the core solution in a class of social decision problems concerning the provision of collective goods (or bads) if the rules are modified to permit sidepayments. In these problems, a kind of formal decision procedure that includes any weighted or unweighted majority rule governs only the decision about collective goods. Each decision about collective goods, however, implies a vector of the agents' endowments of private wealth that can, but need not, vary across the alternatives. Any agent may offer to make sidepayments from this endowment that are contingent on the collective goods decision, but the agent holds preferences that, given any fixed decision about collective goods, strictly increase in the agent's own wealth.