Hiding actions in multi-player games

In the game-Theoretic approach to reasoning about multi-Agent systems, imperfect information plays a key role. It requires that players act in accordance with the information available to them. The complexity of deciding games that have imperfect information is generally worse than those that do not have imperfect information, and is easily undecidable. In many real-life scenarios, however, we just have to deal with very restricted forms of imperfect information and limited interactions among players. In these settings, the challenge is to come up with elementary decision procedures, as we do. We study multi-player concurrent games where (i) Player0's objective is to reach a target W, and (ii) the opponents are trying to stop this but have partial observation about Player0's actions. We study the problem of deciding whether the opponents can prevent Player0 to reach W, by beating every Player0's strategy. We show, using an automata-Theoretic approach that, assuming the opponents have the same partial observation and play under uniformity, the problem is in ExpTime.