1 Hobbes, though in fact he has a use for one version of the first form, argues nevertheless that only the second form can be effective. For him the first form appears in sequence with the second form; and he tends to run the two forms together in his mind, thinking of them as involving one formula, which first displays a blank or placeholder where the names of the person or persons who are to be the sovereign are to be filled in, but which in the end exhibits, in place of the blank or placeholder, the names filled in. Hobbes, Leviathan: cf. the formula of covenant given at the beginning of Chap. XVIII with the formula given in the antepenultimate paragraph of Chap. XVII. Moreover, Hobbes thinks of agreement to having the formula filled in as contemplated (e.g., by majority vote) as committing the agents to accepting the formula filled in. Actually, a separate agreement is required (since the initial agreement, if it is obtained at all, continues only at the pleasure of the parties); and the two steps present separate (though analogous) problems.

2 The second form of contract is of course not to be confused with a form of contract between agents who become subjects and an agent who becomes sovereign over them. Hobbes, followed (for very different reasons) by Rousseau, denies that such a contract makes sense. Leviathan, Chap. XVIII, fourth paragraph; cf. Du contrat social, Livre I, Chap. VII. If the contract is conceived of as purporting to confer unrestricted power on the sovereign — which unrestricted power Hobbes and Rousseau wish (again for very different reasons) to ascribe to the sovereign — I for one would not dispute the point. Like Hume, however, I think there is no reason for thinking that such a contract must purport to confer unrestricted power; and good grounds for thinking that it makes perfect sense if it does not. Hume, , Of the Original Contract, “fifth paragraph (in Essays and Treatises on Several Subjects, London: Cadell, 1777). I need not pursue the issue hereGoogle Scholar.

3 In insisting upon having the agents literally assemble at one place and give simultaneous undertakings, I am forcing a point that the traditional discussions do not settle. Hobbes's words, for example, might possibly bear other interpretations, according to which the undertakings succeed one another in various ways; and he does not require that all the circumscribed agents literally assemble. See especially Leviathan, Chap. XVIII, fifth paragraph. My interpretation however, not only respects best the consideration, prominent in Hobbes's mind, that all the other assembled agents must reciprocate; it is more favorable to his argument. Any arrangement for giving the undertakings consecutively would increase the costs and risks of having a contract, as would having the agents dispersed rather than assembled.

4 Hume, loc. tit.; and his Treatise of Human Nature, Book III, Section VII. 5 Cf. Marx's brief discussion of Rousseau's contrat social in the Grun-drisse. General Introduction. A more extended critique could easily be elaborated along the lines that I have sketched by transposing the points made by such a Marxist writer as Althusser in criticising individualism in economic theory. See passim Louis Althusser and Balibar, Etienne, Lire le Capital, 2 vols. (Paris: Maspero, 1968)Google Scholar.

6 Simmel, Georg, “The Web of Group-Affiliations” tr. Bendix, Reinhard, in Conflict; The Web of Group-Affiliations (Glencoe, III.: The Free Press. 1955)Google Scholar; cf. Philosophic des Geldes, 5th ed. (Berlin: Duncker & Humblot. 1930), Chap. IVGoogle Scholar.

7 Gauthier, David, “Rational Cooperation”, Nous, Vol. VIII, No. I (03 1974), pp. 53–65.CrossRefGoogle Scholar Also idem, “Reason and Maximisation, Canadian Journal of Philosophy, Vol. IV. No. 3 (03 1975), pp. 411–433Google Scholar.

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

9 Locke, Second Treatise of Government, Chap. III, at the end; Chap. IX, at the beginning.

10 Hume, Treatise, Book III, Section II.

11 As Sobel, J. Howard, elaborating a point made by Luce, R. Duncan and Raiffa, Howard, Games and Decisions (New York: Wiley, 1957), pp. 98–99Google Scholar, shows in “The Need for Coercion”, in Pennock, J. R. and Chapman, J. W., eds., Coercion: Nomos XIV (Chicago and New York: Aldine & Atherton, 1972), pp. 148–177Google Scholar.

12 See (after reading the next footnote) Appendix to this paper, infra.

13 To review the motivational question in more technical terms: Each pair of alternating opportunities to forbear and to be compensated can be looked upon as constituting a game similar to Prisoner's Dilemma. (“Sülar” only, because the agents move in turn, rather than simultaneously.) Over the whole series of opportunities, moreover, one agent would gain most if the other agent abided by the convention while he steadily violated it. However, this option is not available over the series as a whole. In a curiously mixed discussion, cited by Sobel, which fails to come to decisive grips with what rational motivation exactly means in such circumstances, Luce and Raiffa do allow for the agents to achieve some of the benefits of cooperation through learning to practice “collusion” even in a game with a known finite number of pairs of stages; and allow that a fully cooperative solution may emerge if the agents do not know when the series will end. (For further discussion, see Appendix.)

14 Les structures élémentaires de la parenté (Paris: P.U.F., 1949)Google Scholar.

15 The assumption is stronger than one that shapes a version of a dilemma called “Hunter's Dilemma” by Sobel and discussed by him in this version, at pp. 168–169, op. cit. There the agents fail to cooperate even though both would do somewhat better if they accepted a division of labour. Under a strong division of labour, none of the agents has an acceptable option outside the one form of cooperation.

16 De la division du travail social (Paris: Alcan, 1902), Chap. VIIGoogle Scholar.

17 Op. cit., p. 95, at top. I have multiplied all the figures by 10.

18 Leviathan, Chap. XVII, second paragraph.

19 The matrix for Farmer's Dilemma looks the same as the matrix for Prisoner's Dilemma, but the figures bear a different interpretation in this sense: Each agent values the cells in accordance with the benefits that they confer in his eyes upon the other agent, i.e., each agent is motivated to act exactly contrary to Shaw's maxim, “Do not do unto others what you would have them do unto you; their tastes may be different.” Sobel, op. cit., at pp. 154–159.

20 The matrix for Hunter's Dilemma, filled out for comparison with the illustration of Prisoner's Dilemma, has a form that can be illustrated as follows:

It is best for both that one hunts while the other returns to tend the campfire, and it does not matter which agent does either task; what both wish to avoid as the worst outcome is the one in which both go on hunting(a ², hi) and the fire goes out for want of tending. Sobel, op. cit., at pp. 159–60.

21 Sobel, op. cit., p. 159 (footnote); p. 164.

22 There are a number of ways of generalizing Prisoner's Dilemma to the n-person case. One can generalize it to all games in which the equilibrium result (the dominant choice for everyone) differs from what (with suitable measures of redistribution at least) would be the optimum result. Schelling, Thomas C. in “Hockey Helmets, Concealed Weapons, and Daylight Saving: A Study of Binary Choices with Externalities”, Journal of Conflict Resolution, Vol. XVII, No. 3 (09 1973), pp. 381–428CrossRefGoogle Scholar, discusses the variety of situations that then have to be considered. Schelling, in exploring this variety, is chiefly interested in such questions as what proportion of agents must make cooperative choices for the optimum to result and how the total payoff at the optimum is divided (before redistribution) between cooperative agents and non-cooperative ones. He leaves unsettled, as a problem of “organization” the question how players are to be assigned to making cooperative and non-cooperative choices. This problem is central for my purposes and remains central under any relevant generalization. It takes the form of demanding that the optimum (or any gains from cooperation less than the optimum) result from the agents' assigning themselves to cooperative or non-cooperative roles. Over the whole range of situations that can plausibly be associated with the traditional problem of the social contract (situations that are instances of what Schelling calls uniform multi-person prisoner's dilemma), the incentive for self-assignment to a cooperative role is, for every agent acting individually, missing. It is no less missing when (as one must realistically allow) the benefits of cooperation — a social contract; a government — can be substantially realized when substantially less than the whole number of agents act cooperatively. Moreover, the problem of getting a majority to enter into the contract and keep it up, if only a majority are required to make it effective, is the same sort of problem, on a smaller scale, as the problem of getting everyone to enter.

23 In his book The Logic of Collective Action (Cambridge, Mass.: Harvard University Press, 1965). See especially the Introduction and the opening passages of Chap. IGoogle Scholar.

24 Ironically, the concept of a public good has often been used to give a purported explanation of the origin or rational foundation of government. Admit- tedly, government is a public good; but it does not follow that rational agents will cooperate in producing it. For a discussion of the general fallacy, see again Olson, loc. cit.; for a discussion concentrating on its use in purported explanations of the existence of governments, a paper by Peter H. Aranson, “Public Goods. Prisoners' Dilemmas, and the Theory of the State”, delivered at the 1974 Annual Meeting of the American Political Science Association (available now in the microfilmed proceedings; to be published elsewhere after revision).

25 Hardin, Russell, in “Collective Action as an Agreeable n-Prisoners' Dilemma”. Behavioral Science, Vol. XVI (1971), pp. 472–481CrossRefGoogle Scholar, has shown that, formally, the circumstances and motivations assumed by Olson's argument can be looked upon precisely as constituting an n-person Prisoner's Dilemma. It seems to me, in fact, that the only formal feature contributed by Olson's assumptions is limiting the difference between the payoff to a given agent when he does not contribute (though everyone else does) and his net payoff when he contributes (along with everyone else) to just the cost of his contribution. Yet the two perspectives are intuitively — shall I say, phenomenologically? — very different. I think most of this difference, perhaps all, may be attributed to the Tact that in the Prisoner's Dilemma perspective one is inclined (misled to a degree by the anecdote that gave the dilemma its name) to stress the agents' fears of being doublecrossed, while in the perspective of Olson's argument about public goods one is inclined to stress the idleness, from any agent's point of view, of making any contribution.

26 Leviathan, Chap. XIII.

27 Cf. Tullock, G., “The Paradox of Revolution”, in Public Choice, Vol. XI (Fall 1971), pp. 89–99CrossRefGoogle Scholar.

28 This suggestion came up during the discussion in Toronto.

29 A hopeful speculation commonly raised by commentators on Prisoner's Dilemma. There is some favorable experimental evidence. See A. Rapport & C. Orwant, “Experimental Games: A Review”, Shubik, Martin, ed.. Game Theory and Related Approaches to Social Behavior (New York: Wiley, 1964), pp. 283–310, at pp. 296–297Google Scholar.

30 This appendix echoes and responds to a discussion at the CPA Institute, and especially to points made by Gauthier and Sobel. I have also had very useful concrete help respecting it from fellow-members of the Aspen/Cornell colloquium on rational choice, especially from Bernard Grofman, who has done extensive original work on iterated Prisoner's Dilemma.