Arrow-Debreu (1954) showed that under conditions of perfect competition, a general equilibrium must exist. But no comparable existence theorem can be found in t

Arrow-Debreu (1954) showed that under conditions of perfect competition, a general equilibrium must exist. But no comparable existence theorem can be found in the various models with imperfect competition. For example, if you remove the condition "no economies of scale," you exclude convex feasible production sets, and you don't get guaranteed existence. Models of imperfect competition need to add other less plausible assumptions to get back existence of equilibrium. (This won't bother Austrian economists or post-Keynesians, because they reject General Equilibrium Theory as misleading and useless anyway. However, these schools of economics don't frame their ideas in mathematics such that it is possible to prove theorems about the existence, uniqueness, and stability of equilibrium.)