  We consider two-player stochastic games played on a finite state space for an
infinite number of rounds. The games are concurrent: in each round, the two
players (player 1 and player 2) choose their moves independently and
simultaneously; the current state and the two moves determine a probability
distribution over the successor states. We also consider the important special
case of turn-based stochastic games where players make moves in turns, rather
than concurrently. We study concurrent games with \omega-regular winning
conditions specified as parity objectives. The value for player 1 for a parity
objective is the maximal probability with which the player can guarantee the
satisfaction of the objective against all strategies of the opponent. We study
the problem of continuity and robustness of the value function in concurrent
and turn-based stochastic parity gameswith respect to imprecision in the
transition probabilities. We present quantitative bounds on the difference of
the value function (in terms of the imprecision of the transition
probabilities) and show the value continuity for structurally equivalent
concurrent games (two games are structurally equivalent if the support of the
transition function is same and the probabilities differ). We also show
robustness of optimal strategies for structurally equivalent turn-based
stochastic parity games. Finally we show that the value continuity property
breaks without the structurally equivalent assumption (even for Markov chains)
and show that our quantitative bound is asymptotically optimal. Hence our
results are tight (the assumption is both necessary and sufficient) and optimal
(our quantitative bound is asymptotically optimal).
