  We study two-player games on finite graphs. Turn-based games have many nice
properties, but concurrent games are harder to tame: e.g. turn-based stochastic
parity games have positional optimal strategies, whereas even basic concurrent
reachability games may fail to have optimal strategies. We study concurrent
stochastic parity games, and identify a local structural condition that, when
satisfied at each state, guarantees existence of positional optimal strategies
for both players.
