In 1925, C. F. Roos published the paper "A Mathematical Theory of Competition" in the American Journal of Mathematics. In that work he introduced dynamic game models as a generalization of the calculus of variations. After this paper, he went further and developed a more detailed mathematical theory for what he called Generalized Lagrange Problems in the Calculus of Variations. These models contained coupled constraints described by nonlinear integral equations.
In this talk we will briefly discuss Roos' competitive equilibrium models and summarize his contributions to the theory of open-loop dynamic games through the use of these general models. We conclude by discussing some preliminary research concerning the existence of open-loop Nash equlibria for problems involving nonlinear integral equations which include Roos' examples as special cases.
Bienvenue à tous!