Efficient, fair, and strategy-proof (re)allocation under network constraints

A resource available in different types is to be distributed or redistributed among agents differing in their ability to consume these types. Preferences over consumption levels are not observable but known to be single-peaked. We identify the only strategy-proof and efficient allocation rule satisfying a formulation of “fair net trades” (Schmeidler and Vind in Econometrica 40(4):637–642, 1972 ). This rule coincides with the “generalized uniform rule” (Thomson in Axiomatic analysis of generalized economies with single-peaked preferences, 1995a ) when the resource is available in a single type and with the “egalitarian rule” (Bochet et al. in J Econ Theory 148:535–562, 2013 ) when there are no individual endowments. Moreover, it coincides with the “uniform rule” (Sprumont in Econometrica 59(2):509–519, 1991 ) when the resource is available in a single type and there are no individual endowments. This rule belongs to a new class of group strategy-proof rules. Our analysis provides a unified treatment of the applications in Bochet et al. (Theor Econ 7:395–423, 2012 , J Econ Theory 148:535–562, 2013 ).