The study of minimax inequalities and applications to economies and variational inequalities. Memoirs of the American Mathematical Society; 625.

This book provides a unified treatment for the study of the existence of equilibria of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities, which strongly depend on his infinite dimensional version of the classical Knaster, Kuratowski and Mazurkiewicz Lemma (KKM Lemma) in 1961. Studied are applications of general system versions of minimax inequalities and generalized quasi-variational inequalities, and random abstract economies and its applications to the system of random quasi-variational inequalities are given. This work: presents new results and recent development of KKM theory; offers an overview of modern and up-to-date treatment of the KKM theory, including related articles covering theory and applications; uses an interdisciplinary approach with specific applications in mathematics and economics; and, includes a comprehensive bibliography.