Equilibrium Theory in Infinite Dimensional Spaces

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The purpose of this monograph is to study several solutionconcepts such as the Walrasian Equilibrium, the Pareto opti-mality, the Core, the Nash Equilibrium and the Correlatedequilibrium in the context of an infinite dimensionalcommodity or strategy space. Of course, the study of theabove equilibrium notions in an infinite dimensionalcommodity or strategy space not only requires noveltechnical arguments and a modification and correction ofmuch of our finite-dimensional intuition about theseconcepts, but this point also goes the other way; asuccessful formulation of the outstanding questions has alsonecessitated the creation of new mathematics. Some of thecontributions in this volume also present a flavor of thesetechnical advances that have been made in the last twentyyears.