Blackwell and Girshick about the concept of strategy:
Imagine that you are to play the White pieces in a single game of chess, and that you discover you are unable to be present for the occasion. There is available a deputy, who will represent you on the occasion, and who will carry out your instructions exactly, but who is absolutely unable to make any decisions of his own volition. Thus, in order to guarantee that your deputy will be able to conduct the White pieces throughout the game, your instructions to him must envisage every possible circumstance in which he may be required to move, and must specify, for each such circumstance, what his choice is to be. Any such complete set of instructions constitutes what we shall call a strategy.
Now think about an infinite game, like repeated prisoner’s dilemma. If we take the idea about strategy as set of instructions seriously then not every function from past histories to an action is something we would like to call a strategy, because not every function can be described by a set of instructions ! This should be clear even before we formalize what instructions mean, simply because the set of possible `instructions’ is countable, as every such instructions is just a sentence in English.
So what should be the formal definition of a strategy in these games, a definition that will capture the intuition of a complete set of instructions that specify what your choice is to be for each possible circumstances? You know what I think.