Abstract
Recent modeling efforts which attempted to apply the classical Nash equilibrium theory were found unsatisfactory because one or more players in the game had nonconvex loss functions (or nonconcave utility functions). In order to handle these difficult and important models, a generalization of the equilibrium is proposed which is denoted the pre-equilibrium set. This set contains all solutions to the first-order necessary optimality conditions for each player's utility function with respect to every opponent's necessary optimality conditions solutions. It contains all the Nash equilibria, as well as other points which may be of interest in their own right.
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