¹ The canonical source is, of course, Luce, R. D. and Raiffa, H., Games and Decisions (New York: Wiley, 1957), pp. 97–104.Google Scholar

² Much mischief might occur if what one player sees as a game initiating a new episode were seen by his opponent as merely another in the previous chain. If players do not perceive the same boundaries of episodes, then ‘episodic games’ such as I shall be discussing risk degenerating into more ordinary ‘iterated games’. The demarcation of episodes is more of a problem in formal models than in real life, however. There interactions are less continuous and naturally fall into more obviously self-contained episodes.

³ These were, of course, John Kennedy's great rules. According to Sorensen, T. D., Kennedy (New York: Harper and Row, 1965), pp. 351–2Google Scholar, ‘Kennedy was not embittered by his legislative defeats. He had no difficulty working with Kerr or Mills or Dirksen the day after they had successfully worked against him, just as his administration had no room for those who had opposed his nomination. He often reminded his wife and brothers not to be bitter against those who fought or failed him, voicing two political maxims: “In politics you have no friends, only allies” and “Forgive but never forget.”’ Sorensen notes that ‘he still remembered, for example, which stores in Boston had accepted window signs for his first congressional campaign and which had refused’.

⁴ Rapoport, A. and Chammah, A., Prisoner's Dilemma (Ann Arbor: University of Michigan Press, 1965)CrossRefGoogle ScholarPubMed; Nicholson, M., Oligopoly and Conflict (Liverpool: Liverpool University Press, 1972)Google Scholar; Goodin, R. E., The Politics of Rational Man (London: Wiley, 1976)Google Scholar; Taylor, M. J., Anarchy and Cooperation (London: Wiley, 1976)Google Scholar; Axelrod, R., ‘Effective Choice in the Prisoner's Dilemma’, Journal of Conflict Resolution, XXIV (1980), 3–23, 379–403CrossRefGoogle Scholar, Axelrod, R. and Hamilton, W. D., ‘The Evolution of Cooperation’, Science, CCXI (1981), 1390–6CrossRefGoogle Scholar; Axelrod, R., ‘The Emergence of Cooperation Among Egoists’, American Political Science Review, LXXV (1981), 306–18.CrossRefGoogle Scholar

⁵ One variation on VTFT is ‘massive retaliation’, punishing every defection with some fixed number (greater than one) of defections of your own. Another variation is ‘graduated response’, punishing each subsequent defection with increasingly more defections of your own (matching the first defection with a single one of your own, the second with two, and so on). Both were represented in Axelrod's Tournament, the latter by ‘Shubik’ in round one and the former by ‘Friedman’ in both rounds. Both are also discussed by Taylor, in Anarchy and Cooperation.Google Scholar

⁶ This cycle sets in with the first defection for ‘massive retaliation’ players, and with the second for ‘graduated response’ ones. This result is demonstrated both in Axelrod's Tournament and in Axelrod and Taylor's proofs.

⁷ This is a slight exaggeration. A TFT player might try defecting on someone he thinks might be a VTFT player, just to make sure he really is a VTFT player rather than someone who is, e.g., programmed to co-operate for the first ten rounds and defect all the rest of the time regardless of what his opponent does. But once the TFT player recognizes the possibility that his opponent might be a VTFT player he will realize that such experiments may entail very high costs. He will, therefore, be very much more reluctant to try an experimental defection after the first hint that his opponent might be a VTFT player.

⁸ In Axelrod's tournament, ‘Tideman/Chieruzzi’ did quite well. It is a ‘graduated-response’ VTFT strategy that tries to build in a ‘fresh start’. In Round 1 this strategy came in second out of fifteen, and in Round 2 ninth out of sixty-three. The only reason it did not do better is, I suspect, that it is very difficult to communicate to certain sorts of opponents that one wants a ‘fresh start’ within the context of an iterated supergame format.

⁹ Rapoport, and Chammah, , Prisoner's Dilemma, p. 196.Google Scholar

¹⁰ If anything, by providing players with more opportunities to switch supergame strategies, the episodic version will increase the need to test one's opponents in this way. Where your opponent appears to have been (and may, therefore, still be) a VTFT player, the extraordinarily high costs of doing so might well dissuade you. But where he seems to be merely a TFT player, such disincentives are greatly diminished.

¹¹ For others, see: Hume, D., A Treatise of Human Nature (London: John Noon, 1739)Google Scholar, Bk. 3, Pt. 2, Sec. 7; Baumol, W. J., Welfare Economics and the Theory of the State, 2nd ed. (London: G. Bell and Sons, 1965), p. 179Google Scholar; Olson, M. Jr., The Logic of Collective Action (Cambridge: Harvard University Press, 1965)Google Scholar; Buchanan, J. M., ‘Ethical Rules, Expected Values and Large Numbers’, Ethics, LXXVI (1965), 1–13CrossRefGoogle Scholar; Frohlich, N. and Oppenheimer, J. A., ‘I Get By With A Little Help From My Friends’, World Politics, XXIII (1970), 104–20CrossRefGoogle Scholar; Goodin, , Politics of Rational ManGoogle Scholar, Ch. 5; Taylor, , Anarchy and CooperationGoogle Scholar; Hardin, R., Collective Action (Baltimore: Johns Hopkins University Press, 1982)Google Scholar, Chs. 3 and 13; Taylor, M. J., Community, Anarchy and Liberty (Cambridge: Cambridge University Press, 1982).CrossRefGoogle Scholar

¹² Even in experimental settings players seize upon ‘obvious’ opportunities for a restart of games. See Rapoport, A. and Dale, P. S., ‘The “End” and “Start” Effects in Iterated Prisoner's Dilemma’, Journal of Conflict Resolution, X (1966), 363–6.CrossRefGoogle Scholar