— Consider the situation in which a decision maker (Actor) has to decide which of several available resources to use in the presence of an adversary (called Controller) that can prevent the Actor of receiving information on the state of some of the resources. The Controller has a limitation on the amount of information it can conceal. What information should it deny from the the Actor? How should the Actor choose a resource as a function of the statistics of the states of the resources and of the non-concealed information on the state of the others. We formulate this problem as a non-zero sum game and transform it into an equivalent zero-sum game. We then propose ways to compute the most harmful behavior of the Controller as well as the best choice of a resource for the Actor, and analyse their complexity. We identify cases in which the exact solution is computationally intractable, and provide approximate solutions with polynomial complexity. We present many motivating examples and ...