  This paper presents a learning dynamic with almost sure convergence guarantee
for any stochastic game with turn-based controllers (on state transitions) as
long as stage-payoffs induce a zero-sum or identical-interest game.
Stage-payoffs for different states can even have different structures, e.g., by
summing to zero in some states and being identical in others. The dynamics
presented combines the classical stochastic fictitious play with value
iteration for stochastic games. There are two key properties: (i) players play
finite horizon stochastic games with increasing lengths within the underlying
infinite-horizon stochastic game, and (ii) the turn-based controllers ensure
that the auxiliary stage-games (induced from the continuation payoff estimated)
are strategically equivalent to zero-sum or identical-interest games.
