Computing Equilibria and Fixed Points: The Solution of Nonlinear Inequalities (Theory and Decision Library C)

Computing Equilibria and Fixed Points is devoted to the computation of equilibria, fixed points and stationery points. This volume is written with three goals in mind: (i) To give a comprehensive introduction to fixed point methods and to the definition and construction of Grbner bases; (ii) To discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; (iii) To introduce several advanced fixed point and stationery point theorems. These methods and topics should be of interest not only to economists and game theorists concerned with the computation and existence of equilibrium outcomes in economic models and cooperative and non-cooperative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations). Preface. 1. Mathematical Preliminaries. 2. Applications in Game Theory and Economics. 3. First Algorithms for Computing Fixed Points. 4. Simplicial Homotopy Algorithms. 5. Variable Dimension Restart Algorithms. 6. An Algorithm for Integer Linear Programming. 7. Refinement and Stability of stationery Points. 8. Computing a Continuum of Zero Points. 9. Computer stationery Points on Polytopes. 10. The Computation of Antipodal Fixed Points. 11. Computing All Roots of Univariate Polynomials. 12. Grbner Bases for Solving Polynomial Systems. 13. Intersection Theory. 14. Sperner Theory. References. Index.