On the Voluntary Provision of Public Goods with Private Information: The Case of 'Weakest-Link' Public Goods

Abstract

We examine the private provision of a public good whose level is determined by the least contribution of individual group members. Nash equilibrium can be efficient when the game is one of full information. This paper introduces private information about the costs of effort and characterizes equilibrium. In general, many Bayesian equilibria exist and even the "best" is inefficient. Equilibrium comparative statics are derived: improvements in the cost of even only one player benefit all, but riskier cost distributions have an ambiguous effect. Even with "weakest-link" public goods, where similarity of preferences would seem to facilitate coordination, increased heterogeneity (riskier distributions of cost) can increase payoffs. Two mechanisms are provided for improving equilibrium efficiency: technology transfer and cheap-talk communication. While substantial welfare gains are possible, examples show that i) technology transfer may be futile if a "regularity" condition identified herein is not satisfied and ii) cheap talk may be useless if the language for communication is not sufficiently rich.

Keywords: weakest link, voluntary provision, public good, interim efficiency, cheap talk

JEL Classification: D61, D82, H41