Table of Contents

Preface; 1. Introduction: models and mathematics; 2. Convexity; 3. Simplexes; 4. Sperner's lemma; 5. The Knaster-Kuratowski-Mazurkiewicz lemma; 6. Brouwer's fixed point theorem; 7. Maximization of binary relations; 8. Variational inequalities, price equilibrium, and complementarity; 9. Some interconnections; 10. What good is a completely labelled subsimplex?; 11. Continuity of correspondences; 12. The maximum theorem; 13. Approximation of correspondence; 14. Selection theorems for correspondences; 15. Fixed point theorems for correspondences; 16. Sets with convex sections and a minimax theorem; 17. The Fan-Browder theorem; 18. Equilibrium of excess demand correspondences; 19. Nash equilibrium of games and abstract economies; 20. Walrasian equilibrium of an economy; 21. More interconnections; 22. The Knaster-Kuratowski-Mazurkiewicz-Shapley lemma; 23. Cooperative equilibria of games; References; Index.

Promotional Information

This book explores fixed point theorems and its uses in economics, co-operative and noncooperative games.

Reviews

'This book provides a clear exposition of the most important results and techniques of fixed point theory with applications to many areas of current interest in analysis … It is a well written book … the material is completed by well collected exercises at the end of every chapter. We have to emphasize also, the accuracy of applications to differential mathematicians interested in functional analysis, operator theory, differential equations and also to students for the first view on the fixed point theory.' Acta Scientiarum Mathematicarum