  Decentralised optimisation tasks are important components of multi-agent
systems. These tasks can be interpreted as n-player potential games: therefore
game-theoretic learning algorithms can be used to solve decentralised
optimisation tasks. Fictitious play is the canonical example of these
algorithms. Nevertheless fictitious play implicitly assumes that players have
stationary strategies. We present a novel variant of fictitious play where
players predict their opponents' strategies using Extended Kalman filters and
use their predictions to update their strategies.
  We show that in 2 by 2 games with at least one pure Nash equilibrium and in
potential games where players have two available actions, the proposed
algorithm converges to the pure Nash equilibrium. The performance of the
proposed algorithm was empirically tested, in two strategic form games and an
ad-hoc sensor network surveillance problem. The proposed algorithm performs
better than the classic fictitious play algorithm in these games and therefore
improves the performance of game-theoretical learning in decentralised
optimisation.
