Abstract. I explore a game theoretic analysis of social interactions in which each agent’s well-being depends crucially on the well-being of another agent. As a result of this, payoffs are interdependent and cannot be fixed, and hence the overall assessment of particular courses of action becomes ungrounded. A paradigmatic example of this general phenomenon occurs when both players are ‘reflective altruists’, in a sense to be explained. I begin by making an analogy with semantic ungroundedness and semantic paradoxes, and then I show how to proceed in order to model such interactions successfully. I argue that we obtain a second order coordination game for subjective probabilities, in which agents try to settle on a single matrix. As we will see, the phenomenon highlights a number of interesting connections among the concepts of self-knowledge, common knowledge and common belief.