Imagine a strategy in an iterated prisoner’s dilemma game called “Pessimistic Tit-for-tat” (PTfT). It is functionally the same as normal Tit-for-tat. The player plays the same move that their opponent played last round. The only difference is that this player plays Defect in the first round instead of Cooperate. If both players play PTfT, they’ll receive the infinite series of (D,D) payoffs. The good news is, if I know that the other player will copy my moves, maintaining defection rarely holds as an equilibrium.
The question stands however, why wouldn’t they start with normal TfT? We might presume that a player who is pessimistic plays PTfT at the outset. They begin with the belief that the other player will play Always Defect (AD). If both players begin with the pessimistic mindset befitting the PTfT strategy then an infinite stream of both defecting is an equilibrium no matter what their discount rate is. Not only that, but given that the players cannot communicate in any way except through the strategies of the game, the stream of (D,D) that both players observe does not refute their initial pessimism. Little does either player know, but if they only took one small leap of faith and played C, just for the heck of it, a window of opportunity and the ability to communicate would open up that could lead both players into each other’s loving arms.
Robert Hardin describes a similar thought experiment in his 2003 book Indeterminacy and Society. The supposedly unique equilibrium of a finitely repeated prisoner’s dilemma is (AD,AD). The trough equilibrium is due to the ability of both players to backwards induct and anticipate the final round of defection, unraveling any prior possible cooperation. Hardin proposes that in the first round, one player plays Cooperate. By making this simple sacrifice, one player has opened up the window of possibility and no longer given the game a strictly determinate outcome. Interestingly enough, this strategy was exactly what was played in a 100 period prisoner’s dilemma game played by Armen Alchian and John D. Williams as recorded in William Poundstone’s Prisoner’s Dilemma. For the remainder of the game the two economists used the two strategies as both a means of punishment and reward as well as a means of communication.
In his 1898 essay “Philosophical Conceptions and Practical Results”, William James attempts to clarify the pragmatic maxim with an example.
“The question, is matter the producer of all things, or is a God there too? would, for example, offer a perfectly idle and insignificant alternative if the world were finished and no more of it to come. Many of us, most of us, I think, now feel as if a terrible coldness and deadness would come over the world were we forced to believe that no informing spirit or purpose had to do with it, but it merely accidentally had come. The actually experienced details of fact might be the same on either hypothesis, some sad, some joyous; some rational, some; odd and grotesque but without a God behind them, we think they would have something ghastly, they would tell no genuine story, there would be no speculation in those eyes that they do glare with. With the God, on the other hand, they would grow solid, warm, and altogether full of real significance. But I say that such an alternation of feelings, reasonable enough in a consciousness that is prospective, as ours now is, and whose world is partly yet to come, would be absolutely senseless and irrational in a purely retrospective consciousness summing up a world already past. For such a consciousness, no emotional interest could attach to the alternative. The problem would be purely intellectual; and if unaided matter could, with any scientific plausibility, be shown to cipher out the actual facts, then not the faintest shadow ought to cloud the mind, of regret for the God that by the same ciphering would prove needless and disappear from our belief.…Accordingly, in every genuine metaphysical debate some practical issue, however remote, is really involved. To realize this, revert with me to the question of materialism or theism; and place yourselves this time in the real world we live in, the world that has a future, that is yet uncompleted whilst we speak. In this unfinished world the alternative of materialism or theism? is intensely practical!”
William James “Philosophical Conceptions and Practical Results”
Now think back to the two pessimistic players. It appears that their pessimism leads them into a trap, and that in their debates about what theory more properly describes the past AD or PTfT, there will be endless pedantic debates. But when each player, iteratively choosing a strategy, must decide whether to remain in their pessimism to a predictable conclusion, or to take a momentary leap of faith, the question of what the other player is truly playing remains a lively and interesting question. So appears the game between man and the theories which he imposes upon his surroundings. As James notes, metaphysical debates remain live practical issues as long as there is a future to keep them alive.