Abstract: The first task of a microeconomic approach to Fair Division is prescriptive: what definition of Fairness is compatible with the other paramount normative concern of Efficiency (Pareto optimality)? Next, to implement a fair and efficient division of the manna, we must take into account the descriptive constraints of Incentive Compatibility.
We discuss two allocation problems where these three requirements are "miraculously" compatible, in sharp contrast to the general impossibility re- sults discvovered in the first three decades of the mechanism design literature.
For details on the two problems see Lecture 1 in this file

References
Ching S .1994. An Alternative Characterization of the Uniform Rule, Soc. Choice Welfare, 40, 57-60
Ghodsi A, Zaharia M, Hindman B, Konwinski A, Shenker S, Stoica I.2011. Dominant Resource Fairness: Fair Allocation of Multiple Resource Types, Proceedings of the 8th USENIX Conference on Networked Systems Design and Implementation (NSDI), 24.37
Moulin H.2017. One-dimensional mechanism design, Theoretical Economics, 12(2), 587-619
Pazner E, Schmeidler D.1978. Egalitarian equivalent allocations: A new concept of economic equity, Quar. J. Econ., 92(4), 671.87
Sprumont Y.1991. The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule, Econometrica, 59, 509-19