Any function from a non-empty polytope into itself that is locally gross direction preserving is shown to have the fixed point property. Brouwer's fixed point theorem for continuous functions is a special case. We discuss the application of the result in the area of non-cooperative game theory.

We study the dynamic taxation of capital and labor in the Ramsey model under the assumption that taxes and public good provision are decided by a self-interested politician who cannot commit to policies. We show that, as long as the discount factor of the politician is equal to or greater than...