Suppose a game is played repeatedly by a finite collection of players. At every step, each player plays his optimal strategy given the observed probabilities of play for the strategies used by the other players. This generates a (time-dependent) map of the joint strategy space into itself known as 'fictitious play'(FP). This map can be approximated by a discontinuous vector field. 'Weak' solutions for this dynamics are defined, and shown to exist and be unique under certain generic conditions.

more »

... hese weak solutions are also shown to be limits of the original discrete dynamics as the step size approaches zero. It is shown that this process lends itself to a reasonable interpretation of bounded rationality in the appropriate context.