A Game-theoretic Interpretation for the Free-rider Problem under the Lindahl Mechanism

An exposition of the free rider problem in a public good economy is presented by the use of a non-cooperative n-person game. It is shown that the personalized Lindahl prices are not the Nash equilibria of the game. 1. It was proved by Foley (1970) that in an economy with public goods there exist Lindahl equilibria and that they are contained in the core of the economy. Unlike in a market of private goods only, different agents must face different prices for each public good under the Lindahl equilibria. However, as is well-known in literature 〔e.g., Buchanan (1968) ), each agent will have an incentive to 'free ride' on the benefit of the public good. As a result the Lindahl mechanism would not work, since no agent would behave as a price-taker for the Lindahl prices. The purpose of this note is to interpret the free rider problem under the Lindahl mechanism in terms of n-person game theory. This approach would be of some use in explaining the nature of the problem. *The author would like to thank Mr. M. Kaneko for helpful comments and suggestions. -45 -