Equilibrium Theory in Infinite Dimensional Spaces

The purpose of this monograph is to study several solution concepts such as the Walrasian Equilibrium, the Pareto optimality, the Core, the Nash Equilibrium and the Correlated equilibrium in the context of an infinite dimensional commodity or strategy space. Of course, the study of the above equilibrium notions in an infinite dimensional commodity or strategy space not only requires novel technical arguments and a modification and correction of much of our finite-dimensional intuition about these concepts, but this point also goes the other way; a successful formulation of the outstanding questions has also necessitated the creation of new mathematics. Some of the contributions in this volume also present a flavor of these technical advances that have been made in the last twenty years.