Abstract We introduce a class of resource games where resources and preferences are described with the language of a resource-sensitive logic. We present two decision problems, the first of which is deciding whether an action profile is a Nash equilibrium. When dealing with resources, interesting questions arise as to whether some undesirable equilibria can be eliminated by a central authority by redistributing the available resources among the agents. We will thus study the decision problem of rational elimination. We will consider them in the contexts of dichotomous or pseudo-dichotomous preferences, and of logics that admit or not the weakening rule. This will offer a variety of complexity results that are applicable to a large number of settings.