I never said that central planning must work better or worse, just that Hayek's reasoning doesn't hold up because it starts from the ridiculous assumption that markets always find the equilibrium, always propagate local knowledge, etc.., and those are the reason why they theoretically are better than planning according to Hayek. I'm arguing against a purely theoretical argument that was cited with purely theoretical reasoning. The source for Hayek's assumptions implying P=NP is this :
https://arxiv.org/pdf/1002.2284I personally don't care for the purely theoretical arguments that Hayek makes, and yes the arguments are full of apriorisms and assumptions but that's the Austrian school for you and that's what you need to prove that markets must be better than planning.
The actual argument I'd make why planning can outperform markets in many industries and cases is pretty straightforward - markets require duplication of labour, they cause intrinsic crashes, they hurt knowledge transfer because they require intellectual property, they require infinite growth, and more.
Meanwhile actual implementations of planning have been plagued by incredibly slow iteration times (in the order of 5-4 years), access to data so horrible that CIA data was sought by planners, excessive centralization due to the impossibility of getting popular input, very low transparency, limitations in processing as data was collected and processed by hand, allocation of resources by hand, etc...
Planning is fundamentally a computer science problem at every level, and every single major defect can be fixed or palliated using techniques developped from computer science.
Because of this and the relative competitiveness, on the order of 1/3, of planning despite horribly deficient implementations, I think that there's a solid shot that planning can be a better solution than markets in most cases, though not all.
Finally, central planning doesn't actually mean eliminating markets - they are still useful for gaging the relative value and demand in consumer goods. Rather, the goal is to replace capital markets.
There, that's my case for why it is very probable that planning can be a better alternative to capitalist markets in most cases.