The Man From the Future: The Visionary Life of John Von Neumann by Ananyo Bhattacharya

Author:Ananyo Bhattacharya [Bhattacharya, Ananyo]
Language: eng
Format: epub
ISBN: 9780241398852
Google: 2ZcbzgEACAAJ
Published: 2021-10-07T03:52:35+00:00

Von Neumann and Morgenstern’s Theory of Games and Economic Behavior appeared in 1944. The first edition promptly sold out – an article about the book on the front page of the New York Times and a dozen glowing reviews in prestigious journals turned the opus into an unlikely best-seller. ‘Ten more such books,’ declared one reviewer, ‘and the progress of economics is assured.’66

Despite the many plaudits, game theory did not immediately catch on with economists. The book was too mathematical. Even at Princeton, where the mathematics department quickly became a hotbed for research on the subject, the economics department was hostile. Personalities played a role. Von Neumann was much admired but, as a non-economist, he was an outsider. Morgenstern’s supercilious manner rubbed many people up the wrong way. ‘The economics department just hated Oskar,’ says economist Martin Shubik, who arrived at Princeton in 1949 expressly to study game theory, ‘not nearly just alone because they couldn’t understand what was going on, but there was a certain aristocratic touch to Oskar, and … that was an extra reason for the hate.’67 Economist Paul Samuelson, a future Nobel laureate, was watching from his berth at MIT. Morgenstern was ‘very Napoleonic’, he later told the historian Robert Leonard, given to making ‘great claims’ that he did not have the wherewithal to prove.68

The main reason for the disdain, though, was that game theory had not yet proved its worth for dealing with economic questions. There were too many loose ends. Top of the list was von Neumann and Morgenstern’s ‘cooperative’ solutions to games with more than two players. Theory of Games assumes that utility can be transferred seamlessly between players in a coalition. This was clearly not true if the ‘gains’ in question are not bundles of cash but troublesome even if they are – a ten-pound note is worth more utils to someone who is homeless than to a millionaire. Moreover, Theory of Games provides no method for calculating how much each player in a coalition should receive: what was a ‘fair’ settlement?

Second, von Neumann and Morgenstern’s ‘stable-set’ solution for the n-person game proved contentious. Did all multi-player games have a cluster of coalitions that could not be disrupted by a member finding a better deal? Von Neumann did not prove it. A quarter of a century after the publication of Theory of Games, mathematician William Lucas would find a ten-person game which had no stable sets at all.69

Many also balked at von Neumann’s approach to non-zero-sum games. The use of a fictitious player, notes mathematician Gerald Thompson, ‘helped but did not suffice for a completely adequate treatment of the non-zero-sum case. This is unfortunate,’ he adds, ‘because such games are the most likely to be found useful in practice.’70

Von Neumann’s biggest blind spot proved to be his failure to consider games in which coalitions were either forbidden or players could not, or simply did not want to, team up. As game theory gained a reputation for a relentless focus on cut-throat competition between calculating individuals, its progenitor did too.

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