Consider the class of games in which each player chooses a strategy from a connected subset of the real line. Many oligopoly models fall into this class. In many of these applications, it would be useful to show that an equilibrium was unique, or at least to have a set of conditions under which...

This paper derives a general sufficient condition for existence and uniqueness in continuous games using a variant of the contraction mapping theorem applied to mapping from a subset of the real line on to itself. We first prove this contraction mapping variant, and then show how the existence...