Generalised weakened fictitious play
David S. Leslie and E. J. Collins
A general class of adaptive processes in games is developed, which significantly
generalises weakened fictitious play (Van der Genugten, 2000) and includes several
interesting fictitious-play-like processes as special cases. The general model is
rigorously analysed using the best response differential inclusion, and shown to converge
in games with the fictitious play property. Furthermore, a new actor–critic process
is introduced, in which the only information given to a player is the reward received
as a result of selecting an action — a player need not even know they are playing
a game. It is shown that this results in a generalised weakened fictitious play
process, and can therefore be considered as a first step towards explaining how players
might learn to play Nash equilibrium strategies without having any knowledge of
the game, or even that they are playing a game.
Some key words:
fictitious play, best response differential inclusion, stochastic
approximation, actor-critic process.