The price of anarchy is a ratio between the efficiency of a centralized solution and a solution with decentralized decision makers. The implicit assumption seems to be that the centralized solution is always at least as efficient as the decentralized solution, due to phenomena such as Braess's Paradox, and thus the ratio must be at least 1. However, it is often said that command economies are less efficient than free market economies. Central planners cannot seem to get the parameters of an economy pinned down effectively, relative to markets under first welfare theorem assumptions about elasticity, market impact, etc. How does this fit into the price of anarchy model? Shouldn't this be a case in which the price of anarchy is less than 1?
A related question, and perhaps even a special case of the above, a lot of macroeconomic models seem to be aimed at getting market outcomes to hug centrally planned outcomes as closely as possible (i.e., the motivation for first welfare theorem conditions), but if centrally planned outcomes empirically appear to be worse, why is the focus not instead on evaluating how centralized systems stack up using market systems as the gold standard? This seems to be closer to how lay persons conceive of the relation between centralized and decentralized economic systems. Is this type of analysis also performed in macroeconomics?