Psychological Game Theory (PGT) expands 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, and also to their beliefs about others' beliefs about their strategies, and so on. This paper argues that, thanks to the epistemic implications 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 related respectively to the role of players' intentionality, to the self-fulfilling nature of trust and finally to the so-called social framing effects.