No CrossRef data available.
Article contents
The Success of Hyperrational Utility Maximizers in Iterated Prisoner's Dilemma: A Response to Sobel*
Published online by Cambridge University Press: 13 April 2010
Extract
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.
- Type
- Articles
- Information
- Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 28 , Issue 2 , Spring 1989 , pp. 265 - 274
- Copyright
- Copyright © Canadian Philosophical Association 1989
References
1 See Hampton, Jean, Hobbes and the Social Contract Tradition (Cambridge, London: Cambridge University Press, 1986), 75–76Google Scholar; Braybrooke, David, “The Insoluble Problem of the Social Contract”, Dialogue 15 (March 1976), 3–37CrossRefGoogle Scholar, reprinted in Campbell, Richmond and Sowden, Lanning, eds., Paradoxes of Rationality and Cooperation (Vancouver, BC: University of British Columbia Press, 1985), 277–306Google Scholar; Farrell, Daniel, “Hobbes as Moralist”, Philosophical Studies 48 (1985), 257–283CrossRefGoogle Scholar; Axelrod, Robert, “Effective Choice in Prisoner's Dilemma”, Journal of Conflict Resolution 24 (1980a), 3–25CrossRefGoogle Scholar; Axelrod, Robert, “More Effective Choice in Prisoner's Dilemma”, Journal of Conflict Resolution 24 (1980b), 379–403CrossRefGoogle Scholar; Axelrod, Robert, “The Emergence of Cooperation Among Egoists”, American Political Science Review 75 (1981a), 306–318CrossRefGoogle Scholar, reprinted in Campbell, and Sowden, , Paradoxes, 320–329Google Scholar; Axelrod, Robert, The Evolution of Cooperation (New York: Basic Books, 1984)Google Scholar; Axelrod, Robert and Hamilton, W. D., “The Evolution of Cooperation”, Science 211 (1981b), 1390–1396CrossRefGoogle ScholarPubMed; Luce, R. Duncan and Raiffa, Howard, Games and Decisions (New York: John Wiley & Sons, 1957), 98Google Scholar. 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), 38–53CrossRefGoogle Scholar. Reprinted in Campbell, and Sowden, , Paradoxes, 306–319.Google Scholar
3 Sobel, , “Utility Maximizers”.Google Scholar
4 Davis, Lawrence, “Prisoners, Paradox and Rationality”, American Philosophical Quarterly 14 (October 1977).Google Scholar
5 Sobel, , “Utility Maximizers”, 40.Google Scholar
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, LeviathanGoogle Scholar 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).CrossRefGoogle Scholar
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, , LeviathanGoogle Scholar, 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. 156–175Google Scholar. Also see Hodgson, D. H., Consequences of Utilitarianism: A Study of Normative Ethics and Legal Theory (Oxford: Clarendon Press, 1967)Google Scholar, esp. chaps. 2 and 4. Also see Sobel, Jordan Howard, “Interaction Problems for Utility Maximizers”, Canadian Journal of Philosophy 4 (June 1975)CrossRefGoogle Scholar. 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), 149–177.Google Scholar