¹ von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior (Princeton: Princeton University Press, 1944)Google Scholar. Readers unfamiliar with game theory can find approachable introductions in Davis, Morton, Game Theory: A Nontechnical Introduction (New York: Basic Books, 1970)Google Scholar and Hamburger, Henry, Games as Models of Social Phenomena (San Francisco: W.H. Freeman and Company, 1979)Google Scholar. The classic survey is Luce, Duncan and Raiffa, Howard, Games and Decisions (New York: John Wiley, 1957)Google Scholar.

² Schelling, Thomas C., The Strategy of Conflict (Oxford: Oxford University Press, 1960)Google Scholar.

³ Braithwaite, R. B., Theory of Games As a Tool for the Moral Philosopher (Cambridge: Cambridge University Press, 1955)Google Scholar.

⁴ Gauthier, David, Morals by Agreement (Oxford: Clarendon Press, Oxford University Press, 1986)Google Scholar.

⁵ Rawls, John, A Theory of Justice (Cambridge: Harvard University Press, 1971)Google Scholar.

⁶ Hardin, Russell, Morality Within the Limits of Reason (Chicago: Chicago University Press, 1988)Google Scholar.

⁷ Anatol Rapoport and Melvin Guyer, “A Taxonomy of 2 × 2 Games,”General Systems, No. 11 (1966) pp. 203–214Google Scholar.

⁸ The phrase “moral mathematics” is due to Parfit, Derek, Reasons and Persons (Oxford: Oxford University Press, 1984), chapter 3Google Scholar. See Arrow, Kenneth, Social Choice and Individual Values (New York: John Wiley, 1951)Google Scholar and Riker, William, Liberalism Against Populism (San Francisco: W.H. Freeman, 1982)Google Scholar for discussions of social choice theory and its implications for the concept of the common interest.

⁹ In particular, see Hardin, Morality Within the Limits of Reason, op. cit., and Gauthier, Morals by Agreement, op. cit. [Game theory] is preeminently a descriptive framework for categorizing social interactions. There is theory in the theory of games, but much of it is mathematical theory that often has little applicability to problems that interest social theorists. Game theory is of great value in social theory primarily because it affords conceptual clarification and descriptive simplification and generalization of problems that interest us…. A strength of game theoretic representations of social interactions is their extraordinary transparency and consequent ease of generalization to structurally similar interaction.¹¹Google Scholar

¹⁰ See Hardin, , Morality Within the Limits of Reason, op. cot. chapter 1, for an excellent discussion of the ways in which the limits to our reason constrain our ability to make ethical judgmentsGoogle Scholar.

¹¹ Ibid., p. 32.Google Scholar

¹² Note that this reasoning about threats, like that earlier in the paragraph which views R as the “winner” if the outcome is (R2, C1), requires a stronger value theory than ordinal evaluation with no interpersonal comparisonsGoogle Scholar.

¹³ See, for instance, David M. Kreps and Robert Wilson, “Sequential Equilibria,”Econometrica, No. 50 (1982) pp. 862–87 and Steven J. Brams and Donald Wittman, “Nonmyopic Equilibria in 2 × 2 Games,”Conflict Management and Peace Science, No. 6 (1981) pp. 39–62Google Scholar.

¹⁴ Parfit, Derek, op. cit., chapter 2Google Scholar.

¹⁵ On the repeated two-person prisoners' dilemma, see Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984)Google Scholar and Taylor, Michael, Anarchy and Cooperation (New York: John Wiley, 1976)Google Scholar. On the n-person prisoners' dilemma, see Hardin, Russell, Collective Action (Baltimore: Johns Hopkins University Press, 1982)Google Scholar and Schelling, Thomas C., “Hockey Helmets, Concealed Weapons, and Daylight Saving: A Study of Binary Choices with Externalities”Journal of Conflict Resolution, No. 17 (1973) pp. 381–428Google Scholar.

¹⁶ Axelrod, , Ibid., p. 110. Note that the first feature requires more than an ordinal value theory in which interpersonal comparisons are not possible. Axelrod mentions specifically that players should avoid seeing games as zero-sum when they are not. A practice of judging one's success relative to others ‘is dangerous in the prisoners’ dilemma context. As he notes, “Asking how well you are doing compared to how well the other player is doing is not a good standard unless your goal is to destroy the other player…. When you are not trying to destroy the other player, comparing your score to the other's score simply risks the development of self-destructive envy.” (p. 111). This caution has direct relevance to assessments of national security, which too often focus on “gaps” between the forces of two nations, a measure that leans strongly in the direction of a form of “envy.”Google Scholar

¹⁷ Ibid., pp. 136–7Google Scholar.

¹⁸ Ibid., pp. 68–9Google Scholar.

¹⁹ Hardin, Russell, “Individual Sanctions, Collective Benefits,” in Campbell, Richmond and Snowden, Lanning, Paradoxes of Rationality and Cooperation (Vancouver: University of British Columbia Press, 1985)Google Scholar.

²⁰ Hardin, Russell, op. cit., chapters 6–14Google Scholar.

²¹ Parfit, Derek, op. cit., pp. 62–66Google Scholar.

²² Axelrod, Robert, op.cit., chapter 7Google Scholar.

²³ Axelrod, Robert, “An Evolutionary Approach to Norms,” American Political Science Review, Vol. 80 (1986) 1095–1112CrossRefGoogle Scholar.

²⁴ For example, See Powell, Robert, “Crisis Bargaining, Escalation, and MAD,” American Political Science Review, Vol. 81 (1987) pp. 717–36CrossRefGoogle Scholar.