How to shake the Invisible Hand (when Robinson meets Friday)
We propose to define the invisible hand by (i) modelling the mechanism itself (not to just assume its existence) and (ii) making explicit the limit conditions for its working. For that purpose, we simply assimilate the working of the invisible hand mechanism to 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 "Robinson case" or social atomicity is just a degenerate feature of a more general requirement that we call the Global 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 (resp. the latter) is sensitive to the latter (resp. the former) in such a way that they exhibit some agreement in preferences. Hence, the "Robinson case" naturally satisfies this property since nor Robinson neither Friday can disagree with himself. But more cooperative situations are also allowed in order to extent the invisible hand mechanism to cases with interactions.
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