Psychological Game Theory (PGT) extends classical game theory allowing for the formal analysis of belief-dependent sentiments and emotions such as resentment, pride, shame, gratefulness, and the like. PGT incorporates these factors by relating agents' subjective expected utility to players' strategies, to their beliefs about others' strategies, but also to their beliefs about others' beliefs about their strategies, and so on. This paper argues that, thanks to the epistemic consequences of this hierarchy of beliefs, PGT is well-endowed to address, and to some extent solve three of the most challenging problems recently emerged in classical game theory, namely, the problem of intentions, that of trust and that of decision frames.