Diploma in Mathematics, University Bonn (Germany), 1971. Doctor in Economics, University Bonn (Germany), 1974. Habilitation, University Bonn (Germany), 1983.
Research assistant Department Economics, Bonn, 1971-1984. Full professor Institute of Mathematics Economics, Bielefeld, Germany, since 1985. Vice-rector Bielefeld University, 1996-1998.
Visiting professor Institute of Mathematics Economics, Bielfeld, 1984-1985, University California, San Diego, 1988-1989, University Arizona, Tucson, 1994-1995, University of California at Los Angeles, 1998-1999. Member advisory board Center for Interdisciplinary Research, Bielefeld, 1991-1993.
Member Deutsche Mathematiker Vereinigung, Econometric Society, Theoretischer Ausschuß des Vereins für Socialpolitik, Society for Advancement of Economic Theory, European Economic Association, Game Theory Society, Society for Economic Design.
Married Monika Trockel Krämer, January 16, 1970. Children: Stefan, Jan, Tobias, Daniel.