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 led to a publication in the 'European Economic Review' (2013). Vol. 61, pp. 186-204.<P> Rational Expectations (RE) models have two crucial dimensions: 1) agents correctly forecast future prices given all available information, and 2) given expectations, agents solve...</p>