1 Axelrod, Robert, The Evolution of Cooperation (New: Basic Books, 1984)Google Scholar. All unadorned page references are to this book.

2 Rapoport, A., Guyer, M., and Gordon, D., The 2 × 2 Game (Ann Arbor, MI: University of Michigan Press, 1976), 343Google Scholar.

3 Our interest lies in contrasting the ethical and moral levels, à strategy used effec-tively by Kalin, J., “Two Kinds of Moral Reasoning: Ethical Egoism as à Moral Theory”, Canadian Journal of Philosophy 5, 323–356.CrossRefGoogle Scholar One could also distinguish, following Dworkin, R. M., “Is Law à System of Rules”, §2, in Dworkin, R., éd., The Philosophy of Law (Oxford: Oxford University Press, 1977),Google Scholar principles from rules, which are definite and apply in “an all-or-nothing fashion” (45). As it turns out, Axelrod's tournament method requires that lower level, or moral, strategies be submit-ted in the form of computer programs. These algorithms are the paradigms of rules. We shall try to impose this welcome standard of clarity, and refer to moral rules in this sense. If anything, there is even more reason to hope that one's first, highest level ethical directive is à rule, since any vagueness or exception would call for yet another, perhaps prior, rule or principle. But we do not want to exclude the case where one has several co-ordinate ethical principles, so we shall use the weaker term for this level.

4 Here we disagree with Kalin's bite-the-bullet defence of Egoism in “Two Kinds”.

5 For example, if co-operation provides 5 to the other player but costs one 2, we get the following matrix, similar in strategic respects to the one we will use throughout:

6 On the IPD's triviality, see Davis, L. H., “Prisoners, Paradox, and Rationality”, American Philosophical Quarterly 14 (1977), 319–327, reprinted with other relevant articles inGoogle ScholarCampbell, R. and Sowden, L., éds., Paradoxes of Rationality and Cooperation (Vancouver, BC: University of British Columbia Press, 1985). On the purported breakdown of rationality in PD, see, as well, J. W. N. Watkins, “Imperfect Ration-ality”, in R. Borger and F. Cioffi, éds., Explanation in the Behavioural Sciences (Cambridge: Cambridge University Press, 1970).Google Scholar On Rapoport confusing IPD and PD, see Barry, B. and Hardin, Russell, éds., Rational Man & Irrational Society (Beverly Hills, CA: Sage, 1982), Epilogue, §5Google Scholar.

7 “For the [IPD] there are four possible outcomes in each move, making 4²⁰⁰ possible games. This is about 10¹²⁰. Forchess, arough estimate is based on 10 possible choices by each player for each of 60 moves, giving (10²)⁶⁰=10¹²⁰”. Axelrod, Robert, “Artificial Intelligence and the Iterated Prisoner's Dilemma”, Discussion Paper No. 120 (Ann Arbor, MI: Institute of Public Policy Studies), 8–9Google Scholar.

8 This revision does not change Axelrod's results significantly. (In the first tournament, i t only reverses the ninth and tenth places.) Note that we will apply this revised Egoistic criterion in our proposed tournament. The elimination of self-play is not à criticism of Axelrod. There is tradeoff between what one builds into the tournament apparatus and what is left to the players. We choose to move from the apparatus to the players something that may beg questions in the context of moral theory.

9 This problem was pressed on me by my colleague Peter Roosen-Runge.

10 The text may misrepresent Axelrod's discussion of TFT and morality by focussing on Universalism for the sake of clarity. Axelrod also discusses à morality of equity, “The insistence on no more than equity is à fundamental property of many rules based upon reciprocity. … TIT FOR TAT won both rounds of the tournament, but it never received more points in any game than the other player! Indeed, it can't possibly score more than the other player in à game because it always lets the other player defect first, and it will never defect more times than the other player does” (137). Once again, we suggest that our ethical/moral distinction will clarify this point. It is remarkable that Egoists should choose such an equitable moral rule as TFT. But it is à distinct question whether players whose first principle was Equality (Treat everyone equally!) should use TFT. A superficial argument that they should not can be based on the following asymmetrical game: Here Row gets more from Co-operation than Column gets. If Column pursues Equality rather than Universal gain, she should Defect on occasion (1/6th of the time) to achieve it. If Row follows TFT, he will punish this righteous Defecting, So perhaps an Ethics of Equity will recommend à variation of TFT, namely, Defect only if the other player is T-P ahead; otherwise C (where T is 5, and P is 0). (Notice that this recommendation is compatible with Axelrod's Characterization Theorem stated on 209–210, which charac-terizes collective stability in terms of not letting the other's cumulative score get too large.) Of course, like all moral (i.e., derivative) recommendations, this one remains to be tested in tournament conditions. In this case, the test would require the introduction of an asymmetrical matrix to distinguish the ethical principle of Equality from Egoism and Universalism.

11 An ecological projection of Axelrod's first tournament (the second would not fit into my very small computer; the extinction pressure was set high also for reasons of size) produced the following after ten generations: Under Egoistic selection, TFT survives with about twice the population/frequency of the original runnerup, TIDEMAN AND CHIERUZZI, while under Universalistic selection, TFT again comes in first, but now the runnerup, again with about half the population/frequency, is the originally third ranking program, NYDEGGER. So the difference between the two selection principles does not undermine TFT's robustness, but does effect the other rules.

12 Cf. Hare, R. M., Moral Thinking (Oxford: Clarendon Press, 1981), chap. 11CrossRefGoogle Scholar.

13 I develop this argument in à review of Singer, Peter, “The Expanding Circle: Ethics and Sociobiology”, Reason Papers 9 (1983), 95–103Google Scholar.

14 Cf. Parfit, D., Reasons and Persons (Oxford: Oxford University Press, 1984), Part 1Google Scholar.

15 Note that some enriched accounts of Egoistic rationality in the PD share this virtue. Cf. Harsanyi, John, Rational Behavior and Bargaining Equilibrium in Games and Social Situations (Cambridge: Cambrige University Press, 1977), chap. 14CrossRefGoogle Scholar.

16 Cf. Kalin, “Two Kinds”, on the Ethic Moral connection in the case of Ethical Egoism. The original inspiration for my account of the extralogical connection between lower and upper levels is Nozick's, Robert discussion of Rawls, Anarchy, State, and Utopia (New York: Basic Books, 1974), 212–213.Google Scholar