How to shake the invisible hand (when Robinson meets Friday)

We propose defining the invisible hand by: (i) modelling the mechanism itself (rather than just assuming its existence); and (ii) making explicit the limit conditions of its working. For that purpose, we simply assimilate the working of the invisible hand mechanism with the existence of a social preference such that individual and social optimalities are consistent. In introducing the possibility of interaction among individuals, we then suggest that the standard "singleton case," or "atomistic individualism," is just an extreme feature of a more general requirement that we call the  network agreement . Our main result is that the invisible hand mechanism does keep on working when there is an interaction between Robinson and Friday if the former (respectively, the latter) is sensitive to the latter (respectively, the former) in such a way that they exhibit some agreement in preferences. Hence, the singleton case naturally satisfies this property because neither Robinson nor Friday can disagree with himself. Further cooperative situations are also allowed in order to extent the invisible hand mechanism to cases with interactions.