2. Philosophy - Stefano Franchi

192
C HESS, GAMES, AND FLIES
and Morgenstern imagine that players may form a plan about their behavior in a game by
deciding, beforehand, which alternative they will choose for each set of alternatives pre-
sented by each move. They call such a plan a strategy. As they observe,
if we require each player to start the game with a complete plan of this
kind, i.e. with a strategy, we by no means restrict his freedom of action. […]
This is because the strategy is supposed to specify every particular decision
only as a function of just that particular amount of actual information which
would be available for this purpose in an actual play (79, my emphasis).
What is peculiar about the definition of strategy, is that the concept of move, with its intrin-
sically related temporal aspect, disappears, at least for any practical purpose. In fact, since
a strategy has to be formed before the player begins to play, and since a strategy is the con-
junction of all the choices that the player will make, it follows, trivially, that the whole
course of action has to be planned beforehand. This conception of strategy differs some-
what from the usual meaning of the term: it is not a general rule of behavior that the player
chooses at the beginning as a general maxim to guide him through the actual mechanisms
of the actual game, when it will be tailored to the specific circumstances. Thus, “take con-
trol of the center” is considered to be a good strategic rule in chess, but its concrete realiza-
tion is not given in advance. Instead, the formulation of a game-theoretic strategy requires
that all possible games must have been plotted in advance in order to select the advanta-
geous from the disadvantageous behaviors. There is no game-theoretic strategy that pre-
scribes to “take control of the center;” rather, there is a set of strategies that describe the
sequence of moves that actually occupy the center. In other words, the concept of strategy
is intrinsically linked to the idea of game as a set including all possible games. It follows
that, in order to choose a strategy, all possible games must have been devised even if the
player is to play a single game. To put it differently, the games as described by von Neu-
mann’s and Morgenstern’s theory are purely static, since the dynamic element of the inter-
action provided by the actual exchange of moves has to be planned before the interaction
starts.