Hayek’s move from economic theory to political philosophy was a natural evolution in his ideas. First, he considered the influence of prices in produ… - Alan O. Ebenstein

During World War II it was exciting and unexpected for Hayek to find someone else, from Vienna, who was interested in many of the same topics that he was. The Open Society and Its Enemies has three main parts, on Plato, Hegel, and Marx. The next main chapters in Hayek’s uncompleted “The Abuse and Decline of Reason,” on which he was at work then, were to be on Hegel and Marx. In addition, Popper’s scholarly style was similar to Hayek’s, with extremely extensive notes.

Hayek truly did get Popper his position at the London School of Economics. “I am personally anxious to get Dr. Popper to this School,” Hayek wrote Gombrich as early as 1943. Given the later prominence that Popper achieved for the school, this was one of Hayek’s most significant contributions to its reputation, as well as the decisive career move in Popper’s life.
Hayek also genuinely influenced Popper’s political philosophy. While Popper always remained to Hayek’s left, he started out much further to Hayek’s left than he wound up, and this movement was in no small part the result of Hayek’s influence. Popper was a charter member of the Mont Pelerin Society. He suggested, however, that socialists be brought into it. Hayek wrote Popper several deeply personal letters in connection with his divorce. It is likely that their personal relationship was more important to and valued by Hayek than Popper, though Popper valued highly Hayek’s friendship.

Hayek expressed more fully and deeply than Mises the epistemological argument for free market order. The crucial issue for Hayek became not that without prices individuals cannot calculate (though he thought this to be the case), but that the division of knowledge renders centralized control of an economy or society impossible.