The Handbook of Mathematical Economics aims to provide a definitive source, reference, and teaching supplement for the field of mathematical economics. It surveys, as of the late 1970's the state of the art of mathematical economics. This is a constantly developing field and all authors were invited to review and to appraise the current status and recent developments in their presentations. In addition to its use as a reference, it is intended that this Handbook will assist researchers and students working in one branch of mathematical economics to become acquainted with other branches of this field.The emphasis of this fourth volume of the Handbook of Mathematical Economics is on choice under uncertainty, general equilibrium analysis under conditions of uncertainty, economies with an infinite number of consumers or commodities, and dynamical systems. The book thus reflects some of the ideas that have been most influential in mathematical economics since the appearance of the first three volumes of the Handbook.

Uncertainty. Incomplete markets (M. Magill, W. Shafer). The theory of value in security markets (D. Duffie). Sunspot equilibria in sequential markets models (P.A. Chiappori, R. Guesnerie). Utility theory with uncertainty (E. Karni, D. Schmeidler). Infinite Economies. Equilibrium theory in infinite dimensional spaces (A. Mas-Colell, W.R. Zame). Overlapping generations (J. Geanakoplos, H. Polemarchakis). Non-Convexity and Imperfect Competition. Equilibrium analysis with non-convex technologies (D. Brown). Monopolistic competition (J.-P. Bénassy). Computation and Mathematical Methods. Computation and multiplicity of equilibria (T. Kehoe). Nonstandard analysis with applications to economics (B. Anderson). Nonlinear dynamical systems: Instability and chaos in economics (W.A. Brock, W.D. Dechert).