On the Computation of Fixed Points in the Product Space of Unit Simplices and an Application to Noncooperative N Person Games

In this paper an algorithm based on the principle of simplicial approximation is introduced to compute fixed points of upper semicontinuous point to set mappings from the product space S of unit simplices into itself. The algorithm is a modification of an algorithm, introduced in an earlier paper. The main feature is that it starts with an arbitrary chosen point in S and that the triangulation of S depends on the starting point. Moreover, the algorithm can terminate with a non-full-dimensional subsimplex, yielding a good approximation. An application is given for non cooperative n person games, where S is the strategy space. Some computational experiences are given.