Well, I enjoyed Finding Equilibrium: Arrow, Debreu, McKenzie and the Problem of Scientific Credit bu Till Düppe and Roy Weintraub. The story is fundamentally simply: Arrow was a sunny-natured genius who excelled in many areas, Debreu a schemer who sought to maximise credit to himself and spent years fretting about whether he would get the Nobel Prize, and McKenzie was unlucky and undeservedly failed to get sufficient credit for his work. The book in the end puts this down to the ‘Matthew effect’, namely that those who are already better known or at more eminent places get greater credit: “for whosoever hath, to him shall be given, and he shall have more abdundance.” Whereas Debreu is (diplomtically) described thus: “His strategizing with respect to credit was the subtlest.”
The work they all did on existence proofs for general equilibrium was ‘in the air’ at the time. All three men had read the same papers, such as the newly-translated work by Abraham Wald, and John Von Neumann’s game theory: “John von Neumann’s authority fused pure mathematics with the eclectic spirit of applied research. The work of McKenzie, Arrow and Debreu would differently make manifest this fusion.” Early biographies treated von Neumann either as the deranged Dr Strangelove or a genius; Düppe and Weintraub cite more recent and more balanced biographies, to which I would add the portrait in George Dyson’s absolutely terrific book about that Princeton milieu, Turing’s Cathedral.
Finding Equilibrium identifies a 1949 conference under the auspices of the Cowles Commission as a launch event for “a new kind of economic theory growing from game theory, operations research and the related mathematical techniques of convex sets, separating hyperplanes and fixed point theory.” (I can’t resist retelling the story of the cookie recipe one of my colleagues put in the Economics Department newsletter when we were suffering through that work ourselves: roll the dough into balls; place the convex sets on a separating hyperplane and bake in a medium oven for 20 minutes.”) The idea was to extend successful wartime planning techniques to a peacetime economy; planning segued from being a political choice to being a question of productive efficiency in a mixed economy.
The conference was multi-disciplinary. “Nearly all the ingredients of an existence proof were on the conference table,” the book notes. Later (1987) Ken Arrow insisted that if he, Debreu and McKenzie hadn’t done the joining together, somebody else would have, using von Neumann’s work along with Tjalling Koopman’s work on production or John Hicks on consumer theory. However, Arrow stands out in this account for the breadth of his interests. “He was unsympathetic to the manner in which such analysis [ie. general equilibrium analysis] was increasingly being used in economic research; the hermetic spirit of such analyses stood in stark contrast to his open, interdisciplinary-cybernetics spirit.” He disliked the use of the Arrow-Debreu theory, concerning perfectly competitive markets, ‘precisely where it is not applicable’.
“For it is not merely that the existence-proof can leave the place of ‘the existent’ undetermined: there need not be any question of such a place.”
The logical demonstration of the existence of equilibrium in the realm of topology is just that.