My interest in non-Archimedean utility theory and the problems related to it was aroused by discussions which I have had with Professors Werner Leinfellner and Gunter Menges. On the occasion of the Second Inter national Game Theory Workshop, Berkeley, 1970, which was sponsored by the National Science Foundation, I had the opportunity to report about a result on non-standard utilities. Work on this subject continued when I was a research assistant of Professor Gunter Menges at the Uni versity of Heidelberg. The present mono graph is essentially a translation of my habilitation thesis which was...