This discussion paper resulted in a publication in the 'SIAM Journal on Optimization', 2006, 16, 854-870. <P> It is well known that an upper semi-continuous compact- and convex-valued mapping fi from a nonempty compact and convex set X to the Euclidean space of which X is a subset has at least one...</p>

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...</p>

This discussion paper resulted in a forthcoming article in the <I>Journal of Economic Behavior & Organization</I>.<P> This paper characterizes the set of equilibrium networks in the two-way flow model of network formation with small decay, and this for all increasing benefit functions of the players. We...</p></i>