DISCUSSION
INFORMATION AND STRATEGY IN ITERATED
PRISONER'S DILEMMA* The prisoner's dilemma (PD)-a two-person, non-zero-sum game-highlights a situation where individual rationality leads to a collectively sub-optimal equilibrium. This has disturbing implications for the social sciences; and the problem has received considerable attention from philosophers, psychologists and economists. It has been used to, interpret Rousseau's concept of the 'general will' and has also cropped up in discussions on ethics and morality 1 . It demonstrates with disconcerting simplicity how atomistic action may lead to collective ill, unless there are binding 'social contracts' to guide individual action.
Respite was sought by pointing out that in reality this game was played more than once; and that could result in the equilibrium from not being the socially inferior one. But it was supposedly demonstrated by Luce and Raiffa 2 (LR) that if the game was repeated a finite number of times, then the equilibrium strategy continued to be the sub-optimal one. It will be argued here that this is not in general so and for their result to hold, it is necessary for certain additional assumptions -which are not required in the non-repeated PD -to be satisfied. These assumptions are highly demanding and proliferate at a remarkable pace as the number of repetitions is increased. This is an optimistic result. It shows that in reality, where this game situation is likely to arise more than once, individual rationality may lead to collective good.
I
The following table is the pay-off matrix for individuals A and B. al, a2 and b~, b2 are possible strategies for A and B respectively, and %] (resp. ~ii) is the pay-off to A (resp. B) for (a i, bi). For simplicity we consider the pay-offs to be monetary payments.