On Extensions of the Cournot-Nash Theorem

Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 244)


This paper is devoted to a problem that occupies a central position in economic theory and whose origins lie in Augustin Cournot’s Recherches sur les Principles Mathématiques de la Théorie des Richesses. The setting is that of a group of players each of which pursues his self-interest as reflected in an individual pay-off function defined on an individual strategy set. What makes the problem interesting is that the optimum choice of any player depends on the actions of all the other players, this dependence being reflected in the pay-off function or in the strategy set or both. As such, this is a problem par excellence in what is now termed non-cooperative game theory.


Banach Space Nash Equilibrium Separable Banach Space Weak Compactness Pure Strategy Equilibrium 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of IllinoisChampaignUSA

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