We critically survey explicit discussions of the narrativity of economic agents by economists. Narrativity broadly refers to the way humans construct and use stories, notably to define their personal identity. We borrow from debates outside of economics to provide the critical dimension of our survey. Most contributions on the narrativity of economic agents do not discuss one another. To establish communication , we suggest a structure of oppositions that characterize these contributions taken as a whole. These oppositions are notably characterized by three tensions: in terms of methodological attitudes ('scientism' vs. 'humanism'), of underlying theories of personal identity postulating the existence of a unique sense of self or not ('diachronicity' vs. 'episodicity') and of the normative implications of narrativity ('welfare-increasing' vs. 'welfare-decreasing'). The main goal is to clarify the structure of opposite positions within a more or less explicit debate about the identity of individuals in economics.