  Solving stochastic games with the reachability objective is a fundamental
problem, especially in quantitative verification and synthesis. For this
purpose, bounded value iteration (BVI) attracts attention as an efficient
iterative method. However, BVI's performance is often impeded by costly end
component (EC) computation that is needed to ensure convergence. Our
contribution is a novel BVI algorithm that conducts, in addition to local
propagation by the Bellman update that is typical of BVI, global propagation of
upper bounds that is not hindered by ECs. To conduct global propagation in a
computationally tractable manner, we construct a weighted graph and solve the
widest path problem in it. Our experiments show the algorithm's performance
advantage over the previous BVI algorithms that rely on EC computation.
