On the uniqueness of Groves mechanisms and the payoff equivalence principle |
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| Institution: | 1. Department of Economics, University of Padua, via del Santo 33, 35123 Padova, Italy;2. School of Social Sciences, University of Manchester, Oxford Road, Manchester M13 9PL, UK;3. Department of Economics, Texas A&M University, College Station, TX 77843, USA;1. Centre of Polymer and Carbon Materials, Polish Academy of Sciences, Curie-Sklodowska 34 St., 41-819 Zabrze, Poland;2. School of Pharmacy with the Division of Laboratory Medicine in Sosnowiec, Medical University of Silesia, Katowice, Poland, Chair and Department of Biopharmacy, Jedno?ci 8, Sosnowiec, Poland;3. Faculty of Mathematics and Natural Sciences, Jan Dlugosz University, Armii Krajowej 13/15, 42-218 Czestochowa, Poland;1. MOVE, Universitat Autònoma de Barcelona, and Barcelona GSE. Departament d’Economia i d’Història Econòmica, Edifici B, 08193 Bellaterra, Spain;2. Departament d’Economia, C/ Universitat de Girona, 10; Universitat de Girona, 17003 Girona, Spain;3. Departamento de Teoría e Historia Económica, Facultad de Ciencias Económicas y Empresariales, Universidad de Málaga, Campus de El Ejido, 29071 Málaga, Spain |
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| Abstract: | Consider a standard mechanism design setting with quasi-linear preferences and private valuations. From Holmström (1979), we know that if the valuations are smooth with respect to types then any efficient, dominant strategy mechanism is in the class of Groves mechanisms. Here I show that, given regular assumptions on the primitives of the design problem, a weaker condition that includes the case of non-smooth valuations is sufficient and necessary for the uniqueness of Groves mechanisms among all efficient, dominant strategy mechanisms. This condition, which imposes a restriction on the behavior of the one-sided directional derivatives of the valuation functions with respect to individual types, is also shown to be sufficient and necessary to obtain the Payoff Equivalence principle for dominant strategy mechanisms whose choice rules are affine maximizers. |
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