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Why Hobbes' State of Nature is Best Modeled by an Assurance Game

  • MICHAEL MOEHLER (a1)
Abstract

In this article, I argue that if one closely follows Hobbes' line of reasoning in Leviathan, in particular his distinction between the second and the third law of nature, and the logic of his contractarian theory, then Hobbes' state of nature is best translated into the language of game theory by an assurance game, and not by a one-shot or iterated prisoner's dilemma game, nor by an assurance dilemma game. Further, I support Hobbes' conclusion that the sovereign must always punish the Foole, and even exclude her from the cooperative framework or take her life, if she defects once society is established, which is best expressed in the language of game theory by a grim strategy. That is, compared to existing game-theoretic interpretations of Hobbes, I argue that the sovereign plays a grim strategy with the citizens once society is established, and not the individuals with one another in the state of nature.

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1 For the interpretation of Hobbes’ state of nature as a one-shot PD game see, for example, Rawls, John, A Theory of Justice (Cambridge, MA, 1971/1999), p. 238; Barry, Brian, Political Argument (London, 1965), pp. 253–4; and Gauthier, David, The Logic of Leviathan (Oxford, 1969), pp. 7980. For the interpretation of Hobbes’ state of nature as an iterated PD game see, for example, Kavka, Gregory, ‘Hobbes's War of All Against All’, Ethics 93 (1983), pp. 291310; Kavka's Hobbesian Moral and Political Theory (Princeton, 1986), pp. 129–36; and Hampton, Jean, Hobbes and the Social Contract Tradition (New York, 1986), pp. 7589. For the interpretation of Hobbes’ state of nature as an assurance dilemma game, see Gregory Kavka, ‘Political Contractarianism’ (unpublished manuscript, 1989) and Vanderschraaf, Peter, ‘War or Peace? A Dynamical Analysis of Anarchy’, Economics and Philosophy 22 (2006), p. 252, with reference to Kavka.

2 See, for example, Skyrms, Brian, ‘The Shadow of the Future’, Rational Commitment and Social Justice, ed. Coleman, Jules L. and Morris, Christopher W. (Cambridge, 1998), pp. 1221; Skyrms’ book, The Stag Hunt and the Evolution of Social Structure (Cambridge, 2004), pp. 1–13; Philip Pettit, Made with Words – Hobbes on Language, Mind, and Politics (Princeton, 2008), pp. 111–14, with reference to Skyrms; and Pärtel Piirimäe, ‘The Explanation of Conflict in Hobbes's Leviathan’, Trames 1 (2006), pp. 3–21.

3 Hobbes, Thomas, Leviathan, ed. Tuck, Richard (Cambridge, 1651/1996), part I, ch. XIII.

4 See Hobbes, Leviathan, part I, ch. XIV.

5 Hobbes argues, however, that rational individuals have certain prudential moral obligations in the state of nature that derive from the laws of nature, which are valid, in foro interno, already in the state of nature, as I will clarify. For a more detailed discussion of this point, see Hobbes, Leviathan, part I, ch. XV and Tom Sorell, ‘Hobbes's Moral Philosophy’, The Cambridge Companion to Hobbes's Leviathan, ed. Patricia Springborg (Cambridge, 2007), pp. 133–5.

6 Hobbes, Leviathan, part I, ch. XI.

7 See Hobbes, Leviathan, part I, ch. XIII. Gregory Kavka argues in ‘Hobbes's War of All Against All’, p. 297, that it is not necessarily rational always to attack first in the state of nature, because if an individual were to behave aggressively as such, she would expose herself to the defensive violence of those attacked. She would identify herself as an especially dangerous person who should be eliminated first. For a further discussion of this point, see also Kavka, Hobbesian Moral and Political Theory, pp. 83–125.

8 Hobbes, Leviathan, part I, ch. XI. See also part I, ch. X.

9 To be clear, prudence itself can be acquired only by past experiences, that is, by looking backwards. A prudent individual analyzes the past with the aim of identifying the relevant causal relationships that govern her empirical and social world in order to make the best decisions today within her forward-looking perspective.

10 Hobbes, Leviathan, part I, ch. XV. I follow David Gauthier's secular reading of Hobbes’ laws of nature, as defended in The Logic of Leviathan, pp. 36–9, 70–1, 178–206, and in ‘Hobbes: The Laws of Nature’, Pacific Philosophical Quarterly 82 (2001), pp. 258–84. According to Gauthier's interpretation, Hobbes’ reference to God as the author of the laws of nature does no essential work in Hobbes’ argument. For a similar view, see also Kavka, Hobbesian Moral and Political Theory, pp. 361–3 and Hampton, Hobbes and the Social Contract Tradition, pp. 94–6.

11 Hobbes uses the term covenant instead of contract in his formulation of the third law of nature. Covenants are a specific type of contract where one or more parties are assumed to perform their parts at some time after the contract is made. For simplicity, I use only the term contract to refer to both concepts, although I use it more often in Hobbes’ strict sense of covenant.

12 See Hobbes, Leviathan, part II, ch. XIX.

13 For support of Hobbes’ conclusion that anarchy leads to a war of (almost) all against all and a more precise description when this conclusion holds, see, for example, Kavka, Hobbesian Moral and Political Theory, pp. 126–56; and Peter Vanderschraaf, ‘War or Peace?’, pp. 243–79 and ‘Game Theory Meets Threshold Analysis: Reappraising the Paradoxes of Anarchy and Revolution’, The British Journal for the Philosophy of Science (2008), pp. 600–6.

14 For an excellent discussion of the key concepts of Hobbes’ moral and political theory and the validity and soundness of his arguments, see, for example, David Gauthier, The Logic of Leviathan; Gregory Kavka, Hobbesian Moral and Political Theory; and Jean Hampton, Hobbes and the Social Contract Tradition.

15 By standard game theory, I mean non-evolutionary game theory. Standard game theory is methodologically more adequate to capture Hobbes’ state of nature argument than evolutionary game theory, because Hobbes’ state of nature serves as a device to justify the absolute sovereign. Hobbes’ project is justificatory and static in the sense that he does not want to provide an evolutionary explanation for the actual existence of the absolute sovereign. David Hume's state of nature argument, for example, is by contrast best modeled by evolutionary game theory, because Hume's genealogy of morals aims to explain the emergence of the existing social and political structure.

16 See Kavka, ‘Hobbes's War of All Against All’, pp. 291–310; Kavka's Hobbesian Moral and Political Theory, pp. 129–36; and Hampton, Hobbes and the Social Contract Tradition, pp. 75–89, for example. See also Kinch Hoekstra, ‘Hobbes on the Natural Condition of Mankind’, The Cambridge Companion to Hobbes's Leviathan, pp. 114–15, for a more general discussion of this idea.

17 See Gregory Kavka, ‘Hobbes's War of All Against All’, pp. 291–310.

18 Hobbes, Leviathan, part I, ch. XIII. For a more detailed discussion of the conditions under which it is rational to cooperate in a finitely repeated PD game, see Sugden, Robert, The Economics of Rights, Co-operation and Welfare (New York, 1986/2004), pp. 111–25.

19 If the assumption of complete information is dropped, then it may be rational for individuals to cooperate in a finitely repeated PD game. In this case, however, the problem of endgame imperfection arises, as Reinhard Selten and Rolf Stoecker have shown in ‘End Behavior in Sequences of Finite Prisoner's Dilemma Supergames: A Learning Theory Approach’, Journal of Economic Behavior and Organization 7 (1986), pp. 47–70.

20 Luce, Robert D. and Raiffa, Howard, Games and Decisions: Introduction and Critical Survey (New York, 1957/1985), p. 98. See also Taylor, Michael, The Possibility of Cooperation (New York, 1987/1995), pp. 82108, who reaches a similar conclusion for infinitely repeated n-person PD games. For a critical analysis of Taylor's results, in particular with regard to large groups, see Molander, Per, ‘The Prevalence of Free Riding’, Journal of Conflict Resolution 36 (1992), pp. 756–71.

21 For this point, see, for example, Axelrod, Robert, ‘The Emergence of Cooperation among Egoists’, The American Political Science Review 75 (1981), pp. 306–18, and his later book, The Evolution of Cooperation (New York, 1984).

22 See, however, Jean Hampton who defends such an interpretation in Hobbes and the Social Contract Tradition, pp. 80–9. I think that Hampton's argument is mistaken for the following reason. Hampton argues that the individuals in Hobbes’ state of nature play an infinitely repeated PD game in which it may be rational to cooperate. However, due to their short-sightedness, the individuals do not adequately consider the long-term benefits of cooperation and, as a consequence, defect in the state of nature. I agree with Hampton's argument that some individuals may misconceive their situation in the state of nature, and consequently defect. However, all other forward-looking individuals who identify the real game in the state of nature do not play a one-shot or iterated PD game. Instead, they play an assurance game, because even if rational individuals are forward-looking and they believe that others are too, they will not generally cooperate with their fellows in Hobbes’ state of nature because of the problem of assurance. The problem of assurance is the main problem of collective action that prevents cooperation in Hobbes’ state of nature, and thus the formation of society. The problem of assurance, however, cannot be adequately modeled by the one-shot or iterated PD game, as I will clarify in section IV.

23 |Cooperate = 4(p) + (−2)(1−p)|Defect = 3p + 0 (1−p)|Equilibrium: Cooperate = Defect | → p = 2/3|

24 Hobbes, Leviathan, part II, ch. XVII.

25 For this point, see also Pettit, Made with Words, pp. 62–6.

26 To clarify, the sovereign herself does not come into power by a contract, but by the individuals’ surrender of their rights of nature, which rational individuals regard as beneficial in the state of nature. That is, the sovereign is not empowered by a contract between the citizens and the leader, but by a self-interested alienation of the individuals’ rights of nature. The individuals give up their rights to govern themselves and transfer them to the sovereign, and in doing so, the sovereign acquires, as a free gift, the power to govern the citizens and to punish them for their failings. The sovereign herself, however, is not bound by any agreement, because she neither transfers any rights to the citizens, nor does she make a contract with them. Instead, the social contract is made among the citizens. The citizens metaphorically promise each other, in bilateral agreements, to obey the sovereign and to keep their private contracts after the sovereign is empowered. For a further discussion of this point, see in particular Kavka, Hobbesian Moral and Political Theory, pp. 304–5. As Kavka notes (p. 386), ‘the parties are bound to their sovereign by a double tie of obligation – by contract, each owes every other citizen obedience to the sovereign, and by the obligation to carry out the terms of a free gift . . ., each directly owes the sovereign obedience’.

27 See Hobbes, Leviathan, part I, ch. XV. For a more detailed discussion of Hobbes’ conception of justice see Hoekstra, ‘Hobbes on the Natural Condition of Mankind’, pp. 120–2.

28 See Hobbes, Leviathan, part I, ch. XIV.

29 Stated differently, in foro interno an individual is obliged to fulfill her part of the contract in the state of nature. In foro externo, however, she is bound to do so only if she can be sure that her opponent fulfills her part, which is the case if her opponent has already performed. Translated into the language of game theory, if the first mover cooperates in an assurance game, it is rational for the second mover also to cooperate.

30 See Hobbes, Leviathan, part I, ch. XIII, for example.

31 For support of this conclusion see Kavka, Hobbesian Moral and Political Theory, pp. 126–78.

32 See Gregory Kavka, ‘Political Contractarianism’ and Vanderschraaf, ‘War or Peace?’, p. 252, with reference to Kavka. Vanderschraaf himself (p. 257) rejects the interpretation of Hobbes’ state of nature as an assurance dilemma game and argues instead for a more general Variable Anticipation Threshold model that relaxes the assumption of common knowledge and allows for a more dynamic evolutionary analysis of Hobbes’ state of nature.

33 Hobbes, Leviathan, part I, ch. XV.

34 Hobbes, Leviathan, part I, ch. XV.

35 For support of Hobbes’ claim that unilateral defection, or offensive violation of agreements, is usually irrational under the circumstances described and the assumption of common knowledge of past behavior, see Vanderschraaf, Peter, ‘Covenants and Reputation’, Synthese 157 (2007), pp. 167–95.

36 For a similar interpretation of Hobbes’ argument see Hampton, Hobbes and the Social Contract Tradition, pp. 80–9. Hampton, however, does not explicitly distinguish between prudent individuals and Fooles, and I think that her short-sightedness account of conflict is mistaken, because it leads her to the wrong game-theoretic interpretation of Hobbes’ state of nature, as indicated in section III.

37 To provide an explanation for this number, let us assume that the Foole expects to gain 6 utils if she free rides without being detected, as reflected by Table 1, and a disutility of −2 utils if her defective behavior is detected because the sovereign takes her life. Now, if the Foole believes that the likelihood of being detected is 3/8, then the one-shot PD game will be transformed into the assurance game that is depicted by Table 2. |p = probability that free riding is detected|3 = (−2)(p) + 6(1−p)|→ p = 3/8|

38 See Skyrms, ‘The Shadow of the Future’ and The Stag Hunt and the Evolution of Social Structure, pp. 1–13.

39 See Gauthier, The Logic of Leviathan, pp. 85–6.

40 Hobbes, Leviathan, part I, ch. XIV.

41 See also Vanderschraaf, ‘War or Peace?’, p. 257, who rejects the assurance dilemma game for his evolutionary analysis of Hobbes’ state of nature for a similar reason.

42 See Hobbes, Leviathan, part II, ch. XVII.

43 See Hampton, Hobbes and the Social Contract Tradition, pp. 147–88.

44 See also Kavka, Hobbesian Moral and Political Theory, pp. 179–88, who argues for a two-stage coordination game that allows rational individuals to institute the sovereign, although Kavka's argument operates at some distance from Hobbes’ text.

45 See Hobbes, Leviathan, part II, ch. XXI.

46 Hobbes, Leviathan, part II, ch. XXVIII.

47 For Hobbes’ justification of the sovereign's right to punish the citizens, see Hobbes, Leviathan, part II, ch. XXVIII; Gauthier, The Logic of Leviathan, pp. 146–9; and Hüning, Dieter, ‘Hobbes on the Right to Punish’, The Cambridge Companion to Hobbes's Leviathan, ed. Springborg, Patricia (Cambridge, 2007), pp. 217–40.

48 For further conceptual and empirical considerations with regard to this point, see Kavka, Hobbesian Moral and Political Theory, pp. 250–4.

49 I assume that the costs for installing and maintaining an optimal enforcement mechanism in this sense are lower than the gains that can be made by the formation of society.

50 Hobbes, Leviathan, part I, ch. XV.

51 Such punishment is legitimate only if an individual possesses the ability to reason, if she acted voluntarily, and if the civil laws clearly state the prohibited actions along with the associated sanctions. For a further discussion of Hobbes’ theory of punishment, see in particular Hüning, ‘Hobbes on the Right to Punish’, pp. 221–9.

52 See Skyrms, ‘The Shadow of the Future’, for example.

53 I think that one can give a coherent reading of Hobbes’ argument in Leviathan, including his reply to the Foole, without introducing the notion of commitment power.

54 See Hobbes, Leviathan, part II, ch. XXVIII.

55 I want to thank Richard Bradley, Jerry Gaus, Alex Voorhoeve, and two anonymous reviewers of this journal for helpful discussions of the material addressed in this article and comments on earlier versions.

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Utilitas
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