On Extensions of the Cournot-Nash Theorem

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 Mathematiques de la Theorie 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.

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