Lecture by William Thomson (University of Rochester) in DeCAn lab

On Wednesday, October 26 the all-Russian seminar "Mathematical methods of decision analysis in economics, finance and politics" was held. Professor William Thomson from the University of Rochester gave a lecture on «Preference manipulations lead to the uniform rule»

Co-authors: Olivier Bochet, Toyotaka Sakai

 

Abstract

For the problem of fully allocating a commodity among agents with single-peaked preferences, it is well-known that the "uniform rule" is robust to \emph{strategic manipulation}. Under efficiency and symmetry, it is in fact the unique strategy-proof rule (Sprumont, 1991; Ching, 1994). We conversely analyze the consequences of strategic manipulation for several large families of rules, defined in terms of natural requirements. Given a rule and a preference profile, we consider the associated direct revelation game, and characterize its equilibrium allocations. Our results are unequivocal: for any rule in these families and for each preference profile, there is a unique (strong) Nash equilibrium allocation and it is the uniform allocation for the profile. In other words, attempts to manipulate lead to the uniform rule.