Game Dynamics and Bounded Rationality - Gottinger, Hans W (Advances in Social Sciences Research Journal, 2018)
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. These 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. Keywords: Games, Dynamic Systems, Complexity, Bounded Rationality.