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Rational Cooperation and the Nash Bargaining Solution


In a recent article, McClennen (Synthese 187:65–93, 2012) defends an alternative bargaining theory in response to his criticisms of the standard Nash bargaining solution as a principle of distributive justice in the context of the social contract. McClennen rejects the orthodox concept of expected individual utility maximizing behavior that underlies the Nash bargaining model in favor of what he calls full rationality, and McClennen’s full cooperation bargaining theory demands that agents select the most egalitarian strictly Pareto-optimal distributional outcome that is strictly Pareto-superior to the state of nature. I argue that McClennen’s full cooperators are best described as reasonable agents whose rationality is constrained by moral considerations and that McClennen’s bargaining theory is moralized in this regard. If, by contrast, the orthodox concept of rationality is assumed and plausible assumptions are made about human nature and social cooperation, then a modified version of the standard Nash bargaining solution, which I call the stabilized Nash bargaining solution (Moehler in Utilitas 22:447–473, 2010), is justified. From the perspective of rational agents, the stabilized Nash bargaining solution can accommodate McClennen’s criticisms of the standard Nash bargaining solution in the context of the social contract and, for such agents, it can serve as a principle of distributive justice in deeply morally pluralistic societies.

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  1. 1.

    See Roemer (1986), for example.

  2. 2.

    See Rawls (1971, p. 116), Sen (1970, p. 21), and Barry (1989, pp. 68–76), for example.

  3. 3.

    Rawls (1971, p. 116).

  4. 4.

    See Braithwaite (1955).

  5. 5.

    In Morals by Agreement (1986), Gauthier aims to justify a bargaining solution that is free from moral considerations. However, as subsequent criticisms have shown (see Goodin 1993, for example), Gauthier’s bargaining theory relies ultimately on substantial moral premises. Such criticisms led Gauthier (1993) to reject his own bargaining theory in favor of the standard Nash bargaining solution, and more recently (2013), his whole social contract theory as initially stated in Morals by Agreement in an attempt to reinstate, under a new name, his principle of minimax relative concession as a principle of distributive justice.

  6. 6.

    For recent discussion of conceptual and empirical problems associated with interpersonal utility comparisons, see Hausman (1995), List (2003), and Rossi (2011).

  7. 7.

    See Kalai (1977).

  8. 8.

    See Binmore (1998, pp. 393–395) and (2010, pp. 296–297).

  9. 9.

    See Hobbes (1651).

  10. 10.

    See McClennen (2012).

  11. 11.

    See Moehler (2010).

  12. 12.

    McClennen (2012, p. 66 and p. 73) follows Rawls (1971, p. 54) with his use of social primary goods as a currency for distributive justice.

  13. 13.

    For related criticisms of the standard Nash bargaining solution, see McClennen (2010, pp. 527–530).

  14. 14.

    See Hobbes (1651).

  15. 15.

    For simplicity, I focus in this article on principles of distributive justice as the only social regulative principles.

  16. 16.

    See McClennen (2012, p. 67 and p. 70).

  17. 17.

    See McClennen (2012, pp. 70–71).

  18. 18.

    The moral ideal of reciprocity, although in a slightly different interpretation, is essential to Rawls’ (1971, pp. 88–90) theory of distributive justice. In his later work, Rawls (2001, pp. 122–124) stresses the moral ideal of reciprocity, inter alia, in his defense of the difference principle.

  19. 19.

    See McClennen (2012, pp. 69–70).

  20. 20.

    See McClennen (2012, pp. 68–69).

  21. 21.

    McClennen (2012, p. 73). See also McClennen (2010, pp. 530–533).

  22. 22.

    See McClennen (2012, p. 77). For a foundational discussion of McClennen’s reasons for rejecting the orthodox concept of rationality, see McClennen (2008).

  23. 23.

    See McClennen (2012, p. 78).

  24. 24.

    For the following discussion, see also McClennen (2008, pp. 371–376) and (2010, pp. 534–539).

  25. 25.

    See McClennen (2012, p. 74). Gauthier (1986, pp. 200–205) assumes a similar disagreement point for his bargaining theory.

  26. 26.

    McClennen (2012, p. 75).

  27. 27.

    McClennen (2012, p. 73).

  28. 28.

    See McClennen (2012, pp. 91–92).

  29. 29.

    For discussion of the distinction between the rational and the reasonable, see Sibley (1953), Rawls (1993), and Gaus (1995).

  30. 30.

    Rawls (1993, p. 51). For a recent discussion of Rawls’ notion of reasonableness, see McMahon (2014).

  31. 31.

    In fact, McClennen (2012, p. 88) rejects Rawls’ distinction between the rational and the reasonable and, in this sense, conflates the two concepts.

  32. 32.

    For a somewhat similar criticism from an evolutionary point of view, see Skyrms (1996, pp. 38–42).

  33. 33.

    Three qualifications apply to the following discussion. First, I do not assume that agents are (always) rational in real life in the idealized way described in this article. I engage in a normative analysis. Second, I assume a society with a fixed and finite number of rational agents whose mental and physical capacities are sufficiently developed. Finally, I do not address potential specific duties of distributive justice that may arise for minors, the elderly, or the handicapped.

  34. 34.

    See Moehler (2010), (2012), and (2013).

  35. 35.

    Moehler (2012, p. 100).

  36. 36.

    See Moehler (2012, pp. 95–97).

  37. 37.

    In Moehler (2010) and (2013), I present two moral justifications for this principle. The first justification employs Rawls’ initial statement of the original position and the second justification employs a combined version of Rawls’ original position and Harsanyi’s equiprobability model. In Moehler (2012), I offer a nonmoral justification for the principle that, like McClennen’s argument for full cooperation bargaining, does not invoke a veil of ignorance and is most relevant for the discussion in this article.

  38. 38.

    For a formal discussion of the precise properties of the stabilized Nash bargaining solution, see Moehler (2010, pp. 466–473).

  39. 39.

    For similar criticism, see Luce and Raiffa (1957, pp. 128–131).

  40. 40.

    See Hobbes (1651, Part 1, Chapter 14).

  41. 41.

    Rawls (2001, p. 130 and p. 162), for example, states this condition explicitly for his theory of justice.

  42. 42.

    For further discussion of this point, see Moehler (2010, pp. 451–452). For a somewhat similar argument for a social minimum, see Kavka (1986, pp. 188–224). In contrast to Kavka, however, I do not assume that (i) agents are ‘disaster avoiders’ in the strict sense defined by Kavka, (ii) agents are ignorant of their social positions for the justification and determination of the social minimum, and (iii) the social minimum concerns only economic welfare.

  43. 43.

    See also McClennen (2012, p. 86).

  44. 44.

    For discussion of the basic features of a potential Hobbesian political system, see Kavka (1986, pp. 224–236).

  45. 45.

    See Rawls (2001, p. 42).

  46. 46.

    See Rawls (1971, p. 126). Relatedly, see also McClennen’s (2012, p. 76, footnote 27) discussion of the concept of desert.

  47. 47.

    For further discussion of the rationale that underlies the derivation of the stabilized Nash bargaining solution and its universalized statement, see Moehler (2010, p. 450) and (2012, pp. 95–101).

  48. 48.

    The resulting form of the state that institutionalizes the demands of the stabilized Nash bargaining solution as a principle of distributive justice may best be described as a minimal (or productivist) welfare state. For this point, see Moehler (2010, pp. 465–466).

  49. 49.

    Hume (1739/40, Book 3, Part 3, Section 7).

  50. 50.

    McClennen (2012, p. 83). I would like to thank two anonymous reviewers of this journal for their helpful comments on this article. In addition, I am very grateful to Edward McClennen, not only for his help with improving my argument in this article and my understanding of the differences between his social contract theory and mine, but also, and more importantly, for his generous intellectual support over many years until his death in 2013.


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Moehler, M. Rational Cooperation and the Nash Bargaining Solution. Ethic Theory Moral Prac 18, 577–594 (2015).

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  • Full rationality
  • Reasonableness
  • Equality
  • Instrumental rationality
  • (Strict) Pareto-optimality
  • (Stabilized) Nash bargaining solution