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Samuelson, "Economics and the History of Ideas," pp. 2, 18. (Blake proverb is from "The Marriage of Heaven and Hell," ca. ) -22- a situation and of their mathematical abstraction or generalization leads us to a broader understanding of contingent events. If Samuelson were stood in the dock for his use of mathematics, beside him would be one of history's greatest mathematizers, von Neumann, and his colleague, Morgenstern, the creators of mathematical game theory, which has become one of the dominant frameworks for analyzing social interactions.

Unless enough others are sure to contribute as well, it is foolish of an altruist to give toward the provision of a collective benefit that cannot be obtained at the price of his contribution alone. Baumol, Welfare Economics, p. 92. 9 William J. Baumol, Welfare Economics and the Theory of the State, pp. 90-93. -21- explanation. Anthony Downs had already fully grasped the logic of collective action in the context of one of the most commonplace of political goods: electoral victory (a problem discussed more fully in chapter 4 under "Step Goods").

In particular, we can probably conclude that cooperativeness will not increase, other things being equal, as n increases beyond 2 (but see chapter 3 for fuller discussion of the effects of increasing n). Some experimental data suggest that about one-half of all players cooperate with, and one-half exploit, a 100 percent cooperative adversary-partner in 2-person Prisoner's Dilemma. 21 In the 10-person Prisoner's Dilemma described above, let us assume that this result would mean that five of the players would not pay even if the other five did pay.

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