Convex Analysis and Mathematical Economics

On February 20, 1978, the Department of Econometrics of the University of Tilburg organized a symposium on Convex Analysis and Mathematical th Economics to commemorate the 50 anniversary of the University. The general theme of the anniversary celebration was "innovation" and since an important part of the departments' theoretical work is con­ centrated on mathematical economics, the above mentioned theme was chosen. The scientific part of the Symposium consisted of four lectures, three of them are included in an adapted form in this volume, the fourth lec­ ture was a mathematical one with the title "On the development of the application of convexity". The three papers included concern recent developments in the relations between convex analysis and mathematical economics. Dr. P.H.M. Ruys and Dr. H.N. Weddepohl (University of Tilburg) study in their paper "Economic theory and duality", the relations between optimality and equilibrium concepts in economic theory and various duality concepts in convex analysis. The models are introduced with an individual facing a decision in an optimization problem. Next, an n­ person decision problem is analyzed, and the following concepts are defined: optimum, relative optimum, Nash-equilibrium, and Pareto-optimum.