COOPERATION AND RECOGNITION. A COMMENT
ON "COOPERATION IN THE PRISONER'S DILEMMA" BY J. V. HOWARD In a recent article in this Journal, J.V. Howard [1] puts forward an interesting idea with respect to the achievement (or "rationality") of cooperation in the PD game. On closer inspection I do not think that the idea provides a sound argument for the choice of the cooperative strategy, although in general I am sympathetic with arguments pointing to the choice of the cooperative strategy in the PD game.
Put in simple terms the author's idea is to apply a version of the Tit-for-Tat strategy, which has turned out to be very successful in the iterated PD game, also to the one-shot PD game.
He does so by introducing a "model" of the PD in which the individual players are substituted by computer programs of two types: the first type embodies the non-cooperative strategy D, the second type is a program which recognizes its own type. If it recognizes that its opponent is identical to itself, it plays C. Otherwise, it plays D. This is called the Mirror strategy program.
Now the author's contention is that the Mirror program will do better than the non-cooperative program, which plays D in all cases, because if there are for instance five non-cooperative programs and five Mirror programs, then one (not all!) non-cooperative program playing once with each of the other four non-cooperative programs and with each Mirror program will get 9 points (using the pay-off matrix [1], p. 203), whereas one Mirror program playing once with every other Mirror program and with each of the five non-cooperative programs will get 13 points. Hence the author's conclusion: under certain assumptions it can be sensible to play cooperatively even in a single-shot PD game. This conclusion is not warranted unless the assumptions are made explicit. If they are spelled out, they prove to be very strong in that they "define away" most of the intricacies of the PD game, such that the author's conclusion may be logically correct, but rather trivial.