Foreword

I first met Kenneth Arrow in 1965, half a lifetime ago. As an undergraduate at Stanford University, I took Ken's graduate advanced mathematical economics course. It was a view into another world, where the precision of mathematics had a compass limited only by imagination. The focus of the course was mathematical general equilibrium theory, presented in part from the working manuscript of Arrow and Hahn's General Competitive Analysis (as Ken lectured from the manuscript the ink on some pages was still wet). As the quarter progressed, I discussed the course's required term paper with Ken (then “Prof. Arrow”) and expressed annoyance with the convexity assumption on preferences in Theory of Value. Ken referred me to a well chosen bibliography including Aumann's measure theoretic work (in working paper form), Shapley and Shubik on approximate cores, and the geometric discussions of J. Rothenberg. He did not suggest that the project under discussion was too ambitious. The term paper became an early draft of my first published work “Quasi-equilibria in markets with non-convex preferences.” The final version benefited from detailed critical correspondence from Robert Aumann and the mathematical innovations of Lloyd Shapley and John Folkman communicated by Shapley. From that beginning there was no turning back. Pure mathematical economic theory seemed the most intellectually challenging and rewarding pursuit one could undertake.