A Nobel prize for John Nash
The author presents the mathematical work of John Nash, who won a Nobel prize in economics in 1994. The prize was awarded for a brief paper in game theory written at age 21 [cf. Proc. Natl. Acad. Sci. 36, 48-49 (1950; Zbl 0036.01104)]. There are exposed the contributions of J. Nash to game theory, geometry and analysis. The author discusses Nash's equilibrium-point theory and his existence theorem. There are motivated the basic concepts, there are described the main techniques and there is commented the impact of his work to the problem of understanding competitive situations. There are also presented the outstanding results of J. Nash in the theory of real algebraic varieties and Riemannian geometry. The proof of his theorem on \(C^1\)-isometrically embedding of a compact Riemannian manifold \((M,g)\) is outlined. The paper contains key references to game theory and applications to economics and a list of the mathematical papers of John Nash.
scientific article; zbMATH DE number 851685
scientific article