Computation of least fixed points

Abstract

Many problems from different areas can be formulated as problems of computing a fixed point of a suitable function. Classical examples include the computation of equilibria for games, price equilibria for markets, and many others. There has been significant progress in understanding better the computational nature of such problems and characterizing their complexity in terms of classes like FIXP, which captures the complexity of the computation of fixed points for general (nonlinear) algebraic functions, with the 3-player Nash equilibrium problem as a prototypical example, and PPAD for the computation of fixed points for piecewise linear functions, with the 2-player Nash equilibrium problem as a prototypical example. © 2012 Springer-Verlag.