The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Mathematical Economics

  • Gerard Debreu
Reference work entry


A summary of the emergence and triumph of mathematical economics. The modern phase was deeply influenced by John von Neumann’s article of 1928 on games and his paper of 1937 on economic growth. His 1944 Theory of Games and Economic Behavior, coauthored by Oskar Morgenstern, went beyond differential calculus and linear algebra and paved the way for the axiomatization of economic theory. This has enabled researchers to use precisely stated and flawlessly proved results, in the quest for the most direct link between the assumptions and the conclusions of a theorem. Economic theory is fated for a long mathematical future.


Activity analysis Allais, M. Samuelson, P. Anderson, R. Arrow, K. Asymptotic equality Aumann, R. Axiomatized theory Brouwer’s fixed point theorem Brown, D. Commodity space Competitive equilibrium Contract curve Convexity Cores Cournot, A. Debreu, G. Differential calculus Econometrics Edgeworth, F. Existence of general equilibrium First theorem of welfare economics Fixed point theorems General equilibrium Geometry Hicks, J. Hyperplanes Implicit prices Kakutani’s fixed point theorem Koopmans, T. Lebesgue measure Linear programming Lyapunov’s theorem Mathematical economics McKenzie, L. Nash, J. Measure theory Minimax theorem Morgenstern, O. Non-standard analysis Pareto, V. Price space Real vector space Robinson, A. Sard’s theorem Scarf, H. Set of negligible agents Shubik, M. Sonnenschein, H. Uncertainty Uniqueness of equilibrium Vind, K. von Neumann, J. von Neumann’s lemma Wald, A. Walras, L. Walras’s Law 

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Gerard Debreu
    • 1
  1. 1.