Consistency and incompleteness in general equilibrium theory

We consider the implications for general equilibrium theory of the problems of consistency and completeness as shown in the Gödel-Rosser theorems of the 1930s. That a rigorous consistent formal system is incomplete poses serious problems for dealing with unresolved problems in a fully formal system such as general equilibrium theory. We review the underlying mathematical issues and apply them to this problem for general equilibrium theory. We also consider alternative approaches such as agent-based modeling founded on empirically estimated behavioral assumptions for agents that may allow for a better way to model non-equilibrium evolutionary economic dynamics.