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.

Most contracts, whether between voters and politicians or between house owners and contractors, are incomplete. "More law," it typically is assumed, increases the likelihood of contract performance by increasing the probability of enforcement and/or the cost of breach. This paper studies a...