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.

In this paper we prove the following fixed point theorem. Consider a non-empty bounded polyhedron P and a function f from P to P such that for every x in P with f(x) not equal to x there is a ball in P around x such that the inner product of f(y)-y and f(z)-z is nonnegative for any two elements...

What explains significant variation across countries in the use of vote buying instead of campaign promises to secure voter support? This paper explicitly models the tradeoff parties face between engaging in vote buying and making campaign promises, and explores the distributional consequences...