A fixed point algorithm with economic applications

A new fixed point algorithm applicable to large scale economic problems is developed. Motivated by successive approximation the algorithm iterates on a convex combination of the traditional price to price map and the identity map. The actual combination used is determined from the convergence error of the previous iteration. The specified convex combination is guaranteed to be a contraction if the original map is Lipschitz continuous and antitonal. These sufficient conditions are shown to be weaker than the contraction requirement. A simple supply-demand example is presented to show the advantages of this algorithm over successive approximation.