Computing Equilibria and Fixed Points: The Solution of Nonlinear Inequalities

This text is devoted to the computation of equilibria, fixed points and stationary points. It has been written with three goals in mind: to give a comprehensive introduction to fixed point methods and to the definition and construction of Grobner bases; to discuss several interesting applications of these methods in the fields of general equilibrium theory, game theory, mathematical programming, algebra and symbolic computation; and to introduce several advanced fixed point and stationary 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 co-operative and non-co-operative games, but also to applied mathematicians, computer scientists and engineers dealing with models of highly nonlinear systems of equations (or polynomial equations).