On the Frequency of Interior Cournot-Nash Equilibria in a Public Good Economy

In a public good economy the distribution of initial income is an important determinant of how many individuals contribute to the public good. For the case when all individuals have identical preferences in this paper a simple formula is derived that describes the proportion of all income distributions for which an interior Cournot-Nash equilibrium will result in which every agent makes a strictly positive contribution to the public good. This formula is then applied to a standard Cobb-Douglas utility function showing that the likelihood of interior Cournot-Nash equilibria falls dramatically when the number of individuals is increased. The implications this result might have for the significance of Shibata-Warr neutrality are finally discussed.