Hobbes, harsanyi and the edge of the abyss

Canadian Journal of Political Science

Volumn 29, Issue 1, 1996, Pages 46-69

  Slomp, Gabriella ^a   La Manna, Manfredi M A ^b  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b UNIVERSITY OF ST ANDREWS   (United Kingdom)

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[No Author keywords available]

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EID: 0039471478     PISSN: 00084239     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0008423900007241     Document Type: Article

References (93)

1. Thomas Hobbes, De Cive, The Clarendon Edition of the Philosophical Works of Thomas Hobbes, Vol. 2, ed. by H. Warrender (Oxford: Clarendon Press, 1983), 130.
2. Gregory Kavka, Hobbesian Moral and Political Theory (Princeton: Princeton University Press, 1986); Jean Hampton, Hobbes and the Social Contract Tradition (Cambridge: Cambridge University Press, 1986); Michael Taylor, The Possibility of Cooperation (Cambridge: Cambridge University Press, 1987); and lain McLean, "The Social Contract in Leviathan and the Prisoner's Dilemma Supergame," Political Studies 29 (1981), 339-51.
3. Gregory Kavka, Hobbesian Moral and Political Theory (Princeton: Princeton University Press, 1986); Jean Hampton, Hobbes and the Social Contract Tradition (Cambridge: Cambridge University Press, 1986); Michael Taylor, The Possibility of Cooperation (Cambridge: Cambridge University Press, 1987); and lain McLean, "The Social Contract in Leviathan and the Prisoner's Dilemma Supergame," Political Studies 29 (1981), 339-51.
4. Gregory Kavka, Hobbesian Moral and Political Theory (Princeton: Princeton University Press, 1986); Jean Hampton, Hobbes and the Social Contract Tradition (Cambridge: Cambridge University Press, 1986); Michael Taylor, The Possibility of Cooperation (Cambridge: Cambridge University Press, 1987); and lain McLean, "The Social Contract in Leviathan and the Prisoner's Dilemma Supergame," Political Studies 29 (1981), 339-51.
5. Gregory Kavka, Hobbesian Moral and Political Theory (Princeton: Princeton University Press, 1986); Jean Hampton, Hobbes and the Social Contract Tradition (Cambridge: Cambridge University Press, 1986); Michael Taylor, The Possibility of Cooperation (Cambridge: Cambridge University Press, 1987); and lain McLean, "The Social Contract in Leviathan and the Prisoner's Dilemma Supergame," Political Studies 29 (1981), 339-51.
6. Patrick Neal, "Hobbes and Rational Choice Theory," Western Political Quarterly 41 (1988), 635-52.
7. Neal argues that "rational choice theory reaps a good less than Hobbes attempted to sow and serves to obscure more than illuminate his teaching" (ibid., 635).
8. Hampton, Hobbes and the Social Contract Tradition.
9. Hobbes compares the state of nature to a state of civil war: "it may be perceived what matter of life there would be, where there were no common power to fear, by the manner of life, which men that have formerly lived under a peaceful government, use to degenerate into, in a civil war" (Thomas Hobbes, Leviathan, Vol. 3 of The English Work of Thomas Hobbes, ed. by W. Molesworth [London: Scientia Aalen, 1962], 114-15). We should stress that our claim to novelty refers to the way in which we use rational-choice theory to show the irrationality of descent into the state of nature. This reading of Hobbes's theory goes back to some of his contemporaries and two recent examples are Russell Hardin, "Hobbesian Political Order," Political Theory 19 (1991), 156-80, and Iain Hampsher-Monk, A History of Modern Political Thought (Oxford: Blackwell, 1992), who calls it the "virtual contract" theory.
10. Hobbes compares the state of nature to a state of civil war: "it may be perceived what matter of life there would be, where there were no common power to fear, by the manner of life, which men that have formerly lived under a peaceful government, use to degenerate into, in a civil war" (Thomas Hobbes, Leviathan, Vol. 3 of The English Work of Thomas Hobbes, ed. by W. Molesworth [London: Scientia Aalen, 1962], 114-15). We should stress that our claim to novelty refers to the way in which we use rational-choice theory to show the irrationality of descent into the state of nature. This reading of Hobbes's theory goes back to some of his contemporaries and two recent examples are Russell Hardin, "Hobbesian Political Order," Political Theory 19 (1991), 156-80, and Iain Hampsher-Monk, A History of Modern Political Thought (Oxford: Blackwell, 1992), who calls it the "virtual contract" theory.
11. Hobbes compares the state of nature to a state of civil war: "it may be perceived what matter of life there would be, where there were no common power to fear, by the manner of life, which men that have formerly lived under a peaceful government, use to degenerate into, in a civil war" (Thomas Hobbes, Leviathan, Vol. 3 of The English Work of Thomas Hobbes, ed. by W. Molesworth [London: Scientia Aalen, 1962], 114-15). We should stress that our claim to novelty refers to the way in which we use rational-choice theory to show the irrationality of descent into the state of nature. This reading of Hobbes's theory goes back to some of his contemporaries and two recent examples are Russell Hardin, "Hobbesian Political Order," Political Theory 19 (1991), 156-80, and Iain Hampsher-Monk, A History of Modern Political Thought (Oxford: Blackwell, 1992), who calls it the "virtual contract" theory.
12. Hobbes, De Cive, 49.
13. John C. Harsanyi, "Games with Randomly Disturbed Payoffs: A New Rationale for Mixed Strategy Equilibrium Points," International Journal of Game Theory 2 (1973), 1-23.
14. The substantive qualitative points we establish in section 4 are unaffected by extending the analysis to N (>2) players. The same does not apply to some of the games examined in section 2, which rely on interpreting Hobbes's model as a compound two-player game.
15. See, for example, Hobbes, De Cive, 177; see also Hobbes, Leviathan, chap. 5, and Thomas Hobbes, The Elements of Law Natural and Politic, ed. by F. Tönnies (2nd ed.; London: F. Cass, 1969), chap. 1.
16. See, for example, Hobbes, De Cive, 177; see also Hobbes, Leviathan, chap. 5, and Thomas Hobbes, The Elements of Law Natural and Politic, ed. by F. Tönnies (2nd ed.; London: F. Cass, 1969), chap. 1.
17. See, for example, Hobbes, De Cive, 177; see also Hobbes, Leviathan, chap. 5, and Thomas Hobbes, The Elements of Law Natural and Politic, ed. by F. Tönnies (2nd ed.; London: F. Cass, 1969), chap. 1.
18. For a formal definition of common knowledge, see Robert Aumann, "Agreeing to Disagree," Annals of Statistics 4 (1976), 1236-39; see also Robert Sugden, "Rational Choice: A Survey of Contributions from Economics and Philosophy," Economic Journal 101 (1991), 751-85. Assumptions IR and CK are part of what Neal (in "Hobbes and Rational Choice Theory") calls "E-rationality."
19. For a formal definition of common knowledge, see Robert Aumann, "Agreeing to Disagree," Annals of Statistics 4 (1976), 1236-39; see also Robert Sugden, "Rational Choice: A Survey of Contributions from Economics and Philosophy," Economic Journal 101 (1991), 751-85. Assumptions IR and CK are part of what Neal (in "Hobbes and Rational Choice Theory") calls "E-rationality."
20. According to Hobbes, the content of the right of nature and of the natural laws can be understood by everybody, and everybody can be assumed to understand it (see Hobbes, Leviathan, chap. 5, especially 144).
21. Hobbes, Leviathan, 110; Hobbes, Elements of Law, 70; and Hobbes, De Cive, 45.
22. Hobbes, Leviathan, 110; Hobbes, Elements of Law, 70; and Hobbes, De Cive, 45.
23. Hobbes, Leviathan, 110; Hobbes, Elements of Law, 70; and Hobbes, De Cive, 45.
24. We ignore the trivial case of total indifference where both P = D and S = W.
25. On the relationship between the CK assumption and Nash equilibrium, see M. Bacharach, "A Theory of Rational Decision in Games," Erkenntnis 27 (1987), 17-55, and Sugden, "Rational Choice."
26. Taylor, The Possibility of Cooperation, and McLean, "The Social Contract," are two loci classici.
27. Taylor, The Possibility of Cooperation, and McLean, "The Social Contract," are two loci classici.
28. See, for example, Hobbes, Leviathan, chap. 6, at 44.
29. Ibid., chap. 13, at 88, emphasis added.
30. That is, a state that, once entered into, cannot be escaped from.
31. As explained in Appendix A, the dotted lines in Figures 4 and 6 refer to a weakly dominated strategy and can be ignored.
32. "[B]ees and ants live sociably one with another (which are therefore by Aristotle numbred amongst Politicall creatures), and yet have no other direction, than their particular judgements and appetites; nor speech, whereby one of them can signifie to another, what he thinks expedient for the common benefit: and therefore some man may perhaps desire to know why mankind cannot do the same" (Hobbes, Leviathan, 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87).
33. "[B]ees and ants live sociably one with another (which are therefore by Aristotle numbred amongst Politicall creatures), and yet have no other direction, than their particular judgements and appetites; nor speech, whereby one of them can signifie to another, what he thinks expedient for the common benefit: and therefore some man may perhaps desire to know why mankind cannot do the same" (Hobbes, Leviathan, 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87).
34. "[B]ees and ants live sociably one with another (which are therefore by Aristotle numbred amongst Politicall creatures), and yet have no other direction, than their particular judgements and appetites; nor speech, whereby one of them can signifie to another, what he thinks expedient for the common benefit: and therefore some man may perhaps desire to know why mankind cannot do the same" (Hobbes, Leviathan, 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87).
35. The first applications of the Prisoner's Dilemma to Hobbes's theory can be found in David Gauthier, The Logic of Leviathan (Oxford: Clarendon Press, 1969), and John Watkins, "Imperfect Rationality," in R. Borger and F. Cioffi, eds., Explanation in the Behavioural Sciences (Cambridge: Cambridge University Press, 1970). In the literature on PD applications to Hobbes's theory, usually only strict inequalities are considered; however, the same substantive outcome obtains even with weak inequalities.
36. The first applications of the Prisoner's Dilemma to Hobbes's theory can be found in David Gauthier, The Logic of Leviathan (Oxford: Clarendon Press, 1969), and John Watkins, "Imperfect Rationality," in R. Borger and F. Cioffi, eds., Explanation in the Behavioural Sciences (Cambridge: Cambridge University Press, 1970). In the literature on PD applications to Hobbes's theory, usually only strict inequalities are considered; however, the same substantive outcome obtains even with weak inequalities.
37. Neal, "Hobbes and Rational Choice Theory," 642.
38. Kavka, Hobbesian Moral and Political Theory, especially 182-88;
39. Hampton, Hobbes and the Social Contract Tradition, 150-60;
40. and Taylor, The Possibility of Cooperation, chaps. 2 and 3.
41. Exceptions are McLean, "The Social Contract," and Robert Sugden, The Economics of Rights, Co-operation and Welfare (Oxford: Blackwell, 1986), who apply the hawk-dove game originally developed by John Maynard Smith and G. R. Price (in "The Logic of Animal Conflict," Nature 246 [1973], 15-18) to Hobbes's state of nature.
42. Exceptions are McLean, "The Social Contract," and Robert Sugden, The Economics of Rights, Co-operation and Welfare (Oxford: Blackwell, 1986), who apply the hawk-dove game originally developed by John Maynard Smith and G. R. Price (in "The Logic of Animal Conflict," Nature 246 [1973], 15-18) to Hobbes's state of nature.
43. Hobbes, Leviathan, chap. 24, at 233, emphasis added; see also chap. 13.
44. Hobbes, De Cive, 33, emphasis added.
45. Hobbes, Elements of Law, 29; Hobbes, De Cive, 74-75, 177;
46. Hobbes, Elements of Law, 29; Hobbes, De Cive, 74-75, 177;
47. and Hobbes, Leviathan, 28-29, 146.
48. "All men [are] not alike affected with the same thing, nor the same man at all times" (Hobbes, Leviathan, 146; see also Hobbes, De Cive, 74, 177).
49. "All men [are] not alike affected with the same thing, nor the same man at all times" (Hobbes, Leviathan, 146; see also Hobbes, De Cive, 74, 177).
50. i. However, in the state of nature as described by Hobbes, it is more likely that players' types are independent.
51. Harsanyi, "Games with Randomly Disturbed Payoffs."
52. See ibid, for a formal statement and proofs.
53. Kavka, Hobbesian Moral and Political Theory, Hampton, Hobbes and the Social Contract Tradition; and Taylor, The Possibility of Cooperation.
54. Kavka, Hobbesian Moral and Political Theory, Hampton, Hobbes and the Social Contract Tradition; and Taylor, The Possibility of Cooperation.
55. Kavka, Hobbesian Moral and Political Theory, Hampton, Hobbes and the Social Contract Tradition; and Taylor, The Possibility of Cooperation.
56. Hobbes, Elements of Law, 188.
57. See F. S. McNeilly, The Anatomy of Leviathan (London: Macmillan, 1968).
58. Thomas Hobbes, Thomas White's De Mundo Examined (Anti-White), ed. by H. Whitmore Jones (Bradford: Bradford University Press, 1976), 408, emphasis added.
59. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
60. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
61. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
62. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
63. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
64. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
65. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
66. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
67. "[N]ecessity of nature maketh men . . . to avoid that which is hurtful; but most of all that terrible enemy of nature, death" (Hobbes, Elements of Law, 71); "[reason] teaches every man to fly a contre-naturall dissolution, as the greatest mischiefe that can arrive to Nature" (Hobbes, De Cive, 27); "for every man is desirous of what is good for him, and shuns what is evill, but chiefly the chiefest of natural evills, which is death" (ibid., 47). See also Hobbes, Elements of Law, 71-72, 94; Hobbes, De Cive, 47, 53; and Hobbes, Leviathan, 329. Only in a few scattered passages of his works does Hobbes put forward a weaker claim on self-preservation by suggesting that a few individuals regard life in dishonour or with scorn or without liberty as not worth living (see Hobbes, Elements of Law, 39, 86; Hobbes, De Cive, 67; and Hobbes, Leviathan, 140).
68. Mountain climbing, for example, is fully compatible with S∞.
69. Attaching an infinitely bad payoff to violent death at the hands of others is equivalent to the following two-stage decision process: first, partition the set of social states into the two disjoint subsets of life-endangering actions (actions that may result in violent death) and non-life-endangering actions; second, define preferences (according to glory) over the latter subset; for details see Gabriella Slomp, "Hobbes's Impossibility Theorem" (mimeographed, University of Wales, Swansea, 1995).
70. See, for example, Hobbes, Elements of Law, 47; Hobbes, De Cive, 43; and Hobbes, Leviathan, 156.
71. See, for example, Hobbes, Elements of Law, 47; Hobbes, De Cive, 43; and Hobbes, Leviathan, 156.
72. See, for example, Hobbes, Elements of Law, 47; Hobbes, De Cive, 43; and Hobbes, Leviathan, 156.
73. Hobbes, Elements of Law, 70-71 ; see also Hobbes, Leviathan, 112.
74. Hobbes, Elements of Law, 70-71 ; see also Hobbes, Leviathan, 112.
75. Ibid., 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87.
76. Ibid., 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87.
77. Ibid., 156; see also Hobbes, Elements of Law, 102, and Hobbes, De Cive, 87.
78. Neal, "Hobbes and Rational Choice Theory."
79. Of course, an infinitely bad payoff violates the assumption of bounded utility and thus it could be argued that it is not surprising that no rational decision making is feasible in Hobbes's characterization of the state of nature. Our response to this line of criticism is as follows. Bounded utility is sufficient, but not necessary, to guarantee the existence of equilibria in mixed strategies in non-cooperative games. Nash Theorem (John Nash, "Equilibrium Points in N-Person Games," Proceedings of the National Academy of Sciences 36 [1950], 48-49) states that if mixed strategies are allowed, then any normal-form finite game has at least one equilibrium. This result depends crucially on the payoff functions being bounded (for an elegant proof, see Theorem 3.1 in James Friedman, Game Theory with Applications to Economic [2nd ed.: Cambridge: MIT Press, 1990]). It is simple to verify that there are cases (Neal's coordination game, B2 and its variant B1, as well as the bees and ants game, D2) that yield mutual avoidance as an equilibrium even if W = W' = -∞.
80. Of course, an infinitely bad payoff violates the assumption of bounded utility and thus it could be argued that it is not surprising that no rational decision making is feasible in Hobbes's characterization of the state of nature. Our response to this line of criticism is as follows. Bounded utility is sufficient, but not necessary, to guarantee the existence of equilibria in mixed strategies in non-cooperative games. Nash Theorem (John Nash, "Equilibrium Points in N-Person Games," Proceedings of the National Academy of Sciences 36 [1950], 48-49) states that if mixed strategies are allowed, then any normal-form finite game has at least one equilibrium. This result depends crucially on the payoff functions being bounded (for an elegant proof, see Theorem 3.1 in James Friedman, Game Theory with Applications to Economic [2nd ed.: Cambridge: MIT Press, 1990]). It is simple to verify that there are cases (Neal's coordination game, B2 and its variant B1, as well as the bees and ants game, D2) that yield mutual avoidance as an equilibrium even if W = W' = -∞.
81. With reference to the payoff rankings listed in Appendix A, cases A1, C1 and C2 (insofar as they assume that S < W) are incompatible with W = -∞. Case A2, which subsumes our assumption on glory insofar as it posits that D > P, shares with our version of Chicken the non-existence of an equilibrium, as can be easily verified.
82. Interestingly, in his translation of Thucydides' History, Hobbes came across what is probably the earliest statement of the Prisoner's Dilemma, that he rendered thus: ∞Everyone supposeth, that his own neglect of the common estate can do little hurt, and that it will be the care of somebody else to look to that for his own good: not observing how by these thoughts of every one in several, the common business is jointly ruined" (Thomas Hobbes, The History of the Grecian War Written by Thucydides and Translated by Thomas Hobbes, Vol. 8 of English Works of Thomas Hobbes [London: John Bohn, 1839], 147); for an analysis of Thucydides' influence on Hobbes, see Gabriella Slomp, "Hobbes, Thucydides, and the Three Greatest Things," History of Political Thought 11 (1990), 565-86.
83. Interestingly, in his translation of Thucydides' History, Hobbes came across what is probably the earliest statement of the Prisoner's Dilemma, that he rendered thus: ∞Everyone supposeth, that his own neglect of the common estate can do little hurt, and that it will be the care of somebody else to look to that for his own good: not observing how by these thoughts of every one in several, the common business is jointly ruined" (Thomas Hobbes, The History of the Grecian War Written by Thucydides and Translated by Thomas Hobbes, Vol. 8 of English Works of Thomas Hobbes [London: John Bohn, 1839], 147); for an analysis of Thucydides' influence on Hobbes, see Gabriella Slomp, "Hobbes, Thucydides, and the Three Greatest Things," History of Political Thought 11 (1990), 565-86.
84. Hobbes, Elements of Law, 73; and Hobbes, De Cive, 49.
85. Hobbes, Elements of Law, 73; and Hobbes, De Cive, 49.
86. Ibid.
87. Hobbes, Elements of Law, 34.
88. Hobbes, Leviathan, 113.
89. In a follow-up to this article, one of us provides a new interpretation of Hobbes's political construct from a fully fledged external-observer perspective (see Slomp, "Hobbes's Impossibility Theorem").
90. We ignore the trivial case P = D, S = W.
91. Gender neutrality is a substantial component of Hobbes's theory; on this, see Gabriella Slomp, "Hobbes and the Equality of Women," Political Studies 42 (1994), 441-52.
92. For a defence of the elimination of weakly dominated strategies, see, for example, Roger Myerson, Game Theory: Analysis of Conflict (Cambridge: Harvard University Press, 1991), Theorem 1.7, 30. The potential problem of eliminating weakly dominated strategies, namely, that the order in which the elimination takes place may affect the resulting equilibrium, simply does not arise in two-strategy games such as those considered here.
93. Pursuing the box-crossing analogy sketched a few lines above, we may say that what matters is going from one side of the box to the opposite side, and that wandering around on the zebra crossings on either side of the box is a waste of time.