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The Success of Hyperrational Utility Maximizers in Iterated Prisoner's Dilemma: A Response to Sobel*

  • Robert A. Curtis (a1)

Several recent commentators have suggested that for fully rational agents who find themselves in iterated prisoner's dilemmas of indefinite length, co-operation is the rational strategy. Their argument is that these fully rational agents can be taught, through the co-operative actions of other agents, to bypass the dominant move of noncooperation and co-operate instead. The proponents of the “teaching strategy” seem to have ignored the compelling argument of Jordan Howard Sobel. While the teaching argument may work for agents who are less than purely rational, Sobel has pointed out that hyperrational utility maximizers cannot be taught; they reason deductively, not inductively, as the “teaching argument” requires.

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1 See Hampton Jean, Hobbes and the Social Contract Tradition (Cambridge, London: Cambridge University Press, 1986), 7576; Braybrooke David, “The Insoluble Problem of the Social Contract”, Dialogue 15 (March 1976), 337, reprinted in Campbell Richmond and Sowden Lanning, eds., Paradoxes of Rationality and Cooperation (Vancouver, BC: University of British Columbia Press, 1985), 277306; Farrell Daniel, “Hobbes as Moralist”, Philosophical Studies 48 (1985), 257283; Axelrod Robert, “Effective Choice in Prisoner's Dilemma”, Journal of Conflict Resolution 24 (1980a), 325; Axelrod Robert, “More Effective Choice in Prisoner's Dilemma”, Journal of Conflict Resolution 24 (1980b), 379403; Axelrod Robert, “The Emergence of Cooperation Among Egoists”, American Political Science Review 75 (1981a), 306318, reprinted in Campbell and Sowden, Paradoxes, 320329; Axelrod Robert, The Evolution of Cooperation (New York: Basic Books, 1984); Axelrod Robert and Hamilton W. D., “The Evolution of Cooperation”, Science 211 (1981b), 13901396; Luce R. Duncan and Raiffa Howard, Games and Decisions (New York: John Wiley & Sons, 1957), 98. I should point out that neither Axelrod nor Luce and Raiffa seem to be considering hyperrational agents. Nevertheless, their work provides insight into the teaching argument.

2 Sobel J. Howard, “Utility Maximizers in Iterated Prisoner's Dilemmas”, Dialogue 15 (March 1976), 3853. Reprinted in Campbell and Sowden, Paradoxes, 306319.

3 Sobel, “Utility Maximizers”.

4 Davis Lawrence, “Prisoners, Paradox and Rationality”, American Philosophical Quarterly 14 (October 1977).

5 Sobel, “Utility Maximizers”, 40.

6 Ibid., 46. Sobel does not contend that reasoning from induction is irrational, simply that it is unnecessary. See Sobel's note, 47.

7 Hobbes Thomas, Leviathan originally published in 1651 (Indianapolis, IN and New York: Bobbs-Merrill, 1958), 107.

8 Kavka Gregory, “Deterrence, Utility and Rational Choice”, Theory and Decision 12 (March 1980).

9 The application of maximin to this situation is questionable at best. Maximin was designed to function under complete uncertainty, and we have at least one piece of probability data, a ranking of the probabilities of possible outcomes. Second, the two worst outcomes are both unacceptable. If maximin was used, it would recommend nonco-operation as in the worst of all possible worlds co-operation would yield the worst outcome. If on the first move a player co-operated, was taken advantage of and then moved nonco-operatively on each consecutive move, that player would lose one additional utile than if he had moved nonco-operatively on the first move. But moving nonco-operatively virtually assures that the player will meet this disastrous outcome. The two magnitudes of the potential disasters are only marginally different, yet the probabilities of them obtaining are significantly different. If on the first move the player co-operates, it is true that the disaster he risks is slightly more disastrous than if he did not co-operate, but the chance that the disaster will obtain is significantly less. Both worst scenarios are unacceptable so maximin offers no desirable outcome. Disaster avoidance, on the other hand, yields advice that will maximize the probability of avoiding all disastrous outcomes, co-operating. It seems then with these pieces of information, disaster avoidance is the most desirable principle of the two given this situation. For a more detailed discussion see ibid., 49–52.

It has been pointed out to me that there is a problem generalizing from the disaster avoidance principle to all prisoner's dilemmas. The loss associated with some prisoner's dilemmas will only be costly, not disastrous, and in these cases the disaster avoidance principle will not apply. The negative payoff for double Break found in the matrix in this paper is essential to the applicability of the disaster avoidance principle. But it seems that in cases like the Hobbesian state of nature this payoff will be negative. A major part of Hobbes's argument against anarchy is that the risk of meeting with an early death in the state of nature is high due to the war of every man against every man; it therefore only makes sense to represent the state of nature as a condition in which one actually looses utility. See Hobbes, Leviathan, chap. 13.

10 To explore all of the possible connections to the issues this paper touches on would lead down a path which is not my intended subject. There are, however, many excellent discussions of hyperrational communities. See Gibbard Allan, Utilitarianism and Coordination (unpublished dissertation, Cambridge, MA: Harvard University, 1971), esp. 156175. Also see Hodgson D. H., Consequences of Utilitarianism: A Study of Normative Ethics and Legal Theory (Oxford: Clarendon Press, 1967), esp. chaps. 2 and 4. Also see Sobel Jordan Howard, “Interaction Problems for Utility Maximizers”, Canadian Journal of Philosophy 4 (June 1975). Also see Sobel, “The Need for Coercion”, in Pennock J. R. and Chapman J. W., eds., Coercion: Nomos XIV (Chicago, IL and New York: Aldine-Atherton, 1972), 149177.

* I would like to thank two referees for Dialogue for their helpful comments on this paper. I am especially grateful to Peter French who has stimulated me at each stage of this paper. My work on this paper was partly supported by the National Endowment for the Humanities.

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Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie
  • ISSN: 0012-2173
  • EISSN: 1759-0949
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