One remark explains how Cournot equilibrium responds to taxation on the duopolists. (To maximize revenue, tax 'em the same) The other remark answers the question, What does Cournot Equilibrium maximize.

We present examples of Nash equilibria that do not vary with the distribution of a parameter across agents and then offer a general theorem that characterizes this independence.

We consider a general model of the non-cooperative provision of a public good. Under very weak assumptions there will always exist a unique Nash equilibrium in our model. A smallredistribution of wealth among the contributing consumers will not change the equilibrium amount of the public good. However, larger redistributions of wealth will change the set of contributors and thereby change the equilibrium provision of the public good. We are able to characterize the properties and the comparative statics of the equilibrium in a quite complete way and to analyze the extent to which government provision of a public good ‘crowds out’ private contributions.

This paper was stimulated by a paper by Peter Ware, who used calculus first-order conditons to show that a redistribution of income that does not change the set of voluntary contributors leaves the supply of public goods unchanged. In general, redistributions can change the set of contributors and also the supply of public goods. But we show that even in the general case there are some remarkably sharp comparative statics results.