Does there exist a mathematical formalization of Hayek's ideas about information and the price system? Hayek's idea, roughly, is that individuals in aggregate have distributed knowledge about their own utility functions and about specific supply-conditions, that no single individual can oversee, and that markets can aggregate this information efficiently, while planning bureau's cannot. 

Does there exist a mathematical formalization of Hayek's ideas about this?
Eric Maskin has a paper called “Friedrich von Hayek and Mechanism Design”, which tries to connect some of Hayek’s ideas to the (formal) theory of mechanism design. This paper, and the references therein, might interest you.