¹ The seminal work in the field appeared in 1944: von Neumann, John and Morgenstern, Oskar, Theory of Games and Economic Behavior (Princeton, 1944)Google Scholar. Since then several other standard works have been published: McKinsey, J. C. C., Introduction to the Theory of Games (New York, 1952)Google Scholar, a basic mathematical text; Williams, J. D., The Compleat Strategyst (New York, 1954)Google Scholar, an effort to popularize the basic concepts; and Luce, Robert and Raiffa, Howard, Games and Decisions (New York, 1957)Google Scholar, a balanced and more up-to-date presentation.

² For a discussion of the general nature of simulation, see Dawson, Richard E., “Simulation in the Social Sciences,” in Guetzkow, Harold, editor, Simulation in Social Science (New York, 1962), pp. 1–15Google Scholar.

³ See McKinsey, , op. cit., p. 4Google Scholar. Some authors have preferred the term “player.”

⁴ Recent contributions along these lines include: Boulding, Kenneth E., Conflict and Defense (New York, 1962)Google Scholar; Deutsch, Karl W., The Nerves of Government (New York, 1962), particularly pp. 51–72Google Scholar; Rapoport, Anatol, Fights, Games and Debates (Ann Arbor, 1960)Google Scholar, and Schelling, Thomas C., The Strategy of Conflict (Cambridge, 1960)Google Scholar.

⁵ Our discussion of the generalization principle is based largely on Singer, Marcus, Generalization in Ethics (New York, 1961)Google Scholar.

⁶ Cf. Hare, R. M., The Language of Morals (London, 1952), who holds that two acts cannot differ only as regards Tightness or goodness, pp. 81, 134, 145, 153Google Scholar.

⁷ Von Neumann, , op. cit., p. 15Google Scholar.

⁸ Ibid.

⁹ The procedure for “a numerical measurement of utilities of an individual depends” upon transitivity and completeness in his system of personal preferences. Ibid., p. 19; also Luce, and Raiffa, , op. cit., pp. 25–37Google Scholar.

¹⁰ Some theorists have also employed a “game tree” technique or other mode of relating various possible outcomes of a game, particularly in the case of nonindependent stochastic games. A matrix, however, is commonly used.

¹¹ A game is said to have a saddlepoint where it is to the advantage of one person always to make the same choice of strategy; it is usually to the advantage of others to respond in anticipation with a similarly fixed choice. Minimax refers to a mixed strategy designed to maximize utility while minimizing its loss.

¹² See Wolff, Robert P., “Reflections on Game Theory and the Nature of Value,” Ethics, LXXII (No. 3), 173Google Scholar.

¹³ Rapoport, , op. cit., p. 226–227Google Scholar. Rapoport finds that the goal of game theory, when applied to human situations, “is a prescription of how a rational player should behave in a given game situation when the preferences of this player and of all the other players are given in utility units.”

¹⁴ Ibid., pp. 173–77; Luce, and Raiffa, , op. cit., pp. 94ff.Google Scholar

¹⁵ Immanuel Kant has aptly described the usefulness of game theory — “skill in the choice of means to one's own greatest well being,” the citation is from Singer, , op. cit., p. 221Google Scholar. Karl Deutsch finds game theory particularly edifying for problems of “how to act prudently under conditions of uncertainty and partial ignorance.” Deutsch, , op. cit., p. 52Google Scholar.

¹⁶ The question of the prisoner's guilt or innocence is not immediately relevant to the prisoner's decision, unless we consider his position with respect to the larger society.

¹⁷ Aumann, Robert J., “The Game of Politics,” World Politics, XIV (1961–1962), 680Google Scholar, deserves credit for suggesting this example.

¹⁸ The strategies pursued by many nations, including specifically the strategy of heavy expenditure on nonproductive military hardware, are also not likely in their real interests, but, nevertheless, may represent the most “rational” strategies in the absence of trust or binding norms.

¹⁹ Singer, it should be noted, does not include good consequences as a basis for moral obligation; see op. cit., pp. 206–07. However, the argument for appealing to good consequences might easily be made, particularly since bad consequences can be judged only relative to what might otherwise be expected (which would be better). Such a use of utilitarianism would resemble the position of Rawl's, John practice concept of rules in “Two Concepts of Rules,” Philosophical Review, XLIV (01, 1955)Google Scholar or Toulmin's, Stephen “restricted utilitarianism” in Reason in Ethics (Cambridge, 1950)Google Scholar.

²⁰ Boulding, , op. cit., p. 57Google Scholar, for instance, specifically characterizes the world reflected in game theory as “Hobbesian.” We would have some reservations about Boulding's claim that “empathy and a community of feeling” are “alien to the theory of games”; this is traditionally, but not inherently the case.

²¹ Singer, , op. cit., p. 156Google Scholar.

²² Ibid., p. 157.

²³ Toulmin, , op. cit., p. 170Google Scholar; also pp. 156–57.

²⁴ In examining problems such as surprise attack and disarmament the need to simulate behavior which is more dynamic in character and allows for parametric changes in the bargaining situation has become apparent, see Schelling, , op. cit., pp. 53–118, 230–254Google Scholar. Karl W. Deutsch has criticized past game theory analyses as lacking this dimension of reality and not providing, therefore, for value responses as well as strategic responses in game situations (graduate lecture, April 8, 1964, Yale University). Cf. Rapoport, , op. cit., pp. 226–242Google Scholar and Deutsch, , op. cit., pp. 57–72Google Scholar. It may be that game theory will never completely satisfy these shortcomings and objections, even after mathematical advances have opened further dimensions in its ability to model situations.

²⁵ Rapoport, , op. cit., p. 177Google Scholar.

²⁶ Aumann, , op. cit., p. 682Google Scholar.

²⁷ Rapoport, , op. cit., pp. 248–306Google Scholar, discusses some of the issues involved in developing communication under the rubric, “The Ethics of Debate.” See Schelling, , op. cit., pp. 140–264Google Scholar also.

²⁸ Singer, , op. cit., p. 308Google Scholar.