Strategy-Proof Probabilistic Mechanisms in Economies with Pure Public Goods

1 1 The authors thank the Indian Statistical Institute at New Delhi and the Faculty of Economics and Business Administration of the University of Maastricht for their hospitality. Thanks are also due to Lars Ehlers, Ton Storcken, and the anonymous referees for helpful suggestions. Public good economies where agents are endowed with strictly convex continuous single-peaked preferences on a convex subset of Euclidean space are considered. Such an economy arises for instance in the classical problem of allocating a given budget to finance the provision of several public goods where the agents have monotonically increasing strictly convex continuous preferences. A probabilistic mechanism assigns a probability distribution over the feasible alternatives to any profile of reported preferences. The main result of the paper establishes that any strategy-proof (in the sense of A. Gibbard, Econometrica 45 (1977), 665–681) and unanimous mechanism must be a random dictatorship.