What empire competed economically with Rome? Honestly curious.
Economically, none. Militarily, plenty. The thing is, my dear "free" trade advocate, military protection costs money that isn't found in analyses of "comparative advantage."
Rome imploded economically until it was unable to finance and staff its own military protection. They had to rely increasingly upon slavery, and imported goods to keep things cheap, and a welfare state to manage the citizenry displaced by those cheap goods and services: free food, entertainment, etc. They had the whole kaboodle we are getting with Americans funding globalization via military protection, functioning as a massive subsidy to outsourcing, essentially socializing the risk to delivery of those goods and protecting those investments abroad on the backs of the taxpayers being displaced by those investments.
Because of the resulting welfare state, without the funds to finance the military, they had to outsource that too, just as is being proposed in Congress now to a standing UN army.
Hence the fall.