Advanced Fixed Point Theory for Economics

Beginning with Brouwer's fixed point theorem, and continuing for much of the twentieth century, mathematicians developed an elaborate and beautiful theory of the fixed points of functions from a topological space to itself. Economists have known, since the work on Nash on game theory, and the work of Arrow and Debreu on general equilibrium theory, that this theory was the mathematical foundation for the central models of economic theory, but the advanced portions of the theory have been inaccessible to them, being to some extent scattered in the literature, and dependent on mathematical background in algebraic topology that is unfamiliar to most economists. Presuming only mathematics that is familiar to all theoretical economists, Advance Fixed Point Theory for Economics develops the central aspect of the theory, the topological fixed point index, to maximal generality, emphasizing correspondences and other aspects of the theory that are of special interest to economics. Numerous topological consequences are presented, along with important implications for dynamical systems. Much of the mathematics covered here is broadly applicable in economic modelling. An introductory chapter provides statements of the main results that are sufficient for many applications, and a broad overview of the subject that prepares the reader for the body of the text. Graduate students and researchers in economics, and related fields in mathematics and computer science, will benefit from this book, both as a useful reference and as a well written rigorous exposition of foundational mathematics.

Last updated on October 8, 2020.