with wild abandon. In the biological world, such complexity is messy and unpredictable, and for that sort of thing you need no designer at all, just simple rules governing how a system evolves over time (and some of those rules might be provided by game theory). A Swiss watch, on the other hand, does not evolve over time—it just tells time. And it has no offspring, only springs.

  

19. Gould, Evolutionary Theory, p. 124.

  

20. Of course, had Einstein introduced relativity in a book, instead of writing scientific papers, the 20th century would have had a similar masterpiece.

VON NEUMANN’S GAMES

  

1. Maria Joao Cardoso De Pina Cabral, “John von Neumann’s Contribution to Economic Science,” International Social Science Review, Fall–Winter 2004. Available online at http://www.findarticles.com/p/articles/mi_m0IMR/is_3-4_79.

  

2. Jeremy Bentham, An Introduction to the Principles of Morals and Legislation, Clarendon Press, Oxford, 1907 (1789), Chapters I, III. While written in 1780 and distributed privately, it wasn’t published until 1789.

  

3. Jeremy Bentham, A Fragment on Government, London, 1776, Preface. Available online at http://www.ecn.bris.ac.uk/het/bentham/government.htm. Although Bentham is sometimes credited with coining this phrase, a very similar expression was authored by the Irish philosopher Francis Hutcheson in 1725: “That action is best which procures the greatest happiness for the greatest numbers.”

  

4. Bernoulli suggested that the utility of an amount of money diminished as the logarithm of the quantity, and logarithms do increase at a diminishing rate as a quantity gets larger. But there was no other basis for determining that the logarithmic approach actually quantified anybody’s utility accurately.

  

5. Strictly speaking, utility theory can be used without game theory to make economic predictions, and it often is. But before game theory came along, the mathematical basis of utility was less than solid. In formulating game theory, von Neumann and Morgenstern developed a method to compute utility with mathematical rigor. Utility theory on its own can be used by individuals making solitary decisions, but when one person’s choice depends on what others are choosing, game theory is then necessary to calculate the optimum decision.

  

6. See Ulrich Schwalbe and Paul Walker, “Zermelo and the Early History of Game Theory,” Games and Economic Behavior, 34 (January 2001): 123–137.

  

7. The term “minimax” refers to the game theory principle that you should choose a strategy that minimizes the maximum loss you will suffer no matter what strategy your opponent plays and maximizes the minimum gain you can attain when choosing from each possible strategy.

  

8. In 1937, von Neumann published another influential paper, not specifically linked to game theory, that presented a new view on the nature of growth



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