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On the uniqueness of Groves mechanisms and the payoff equivalence principle. (English) Zbl 1202.91071
This paper establishes a necessary and sufficient condition for uniqueness of Groves mechanisms among efficient, dominant strategy mechanisms in a social choice setting with quasi linear preferences, private valuations and arbitrary sets of alternatives, 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. Potential applications include models with uncountable sets of social alternatives, e.g., public goods provision problems and auction design with divisible objects.

MSC:
91B14 Social choice
91A10 Noncooperative games
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[1] Bergemann, D.; Välimäki, J., Information acquisition and efficient mechanism design, Econometrica, 70, 3, 1007-1033, (2002) · Zbl 1121.91342
[2] Bikhchandani, S.; Chatterji, S.; Lavi, R.; Mu’alem, A.; Nisan, N.; Sen, A., Weak monotonicity characterizes deterministic dominant-strategy implementation, Econometrica, 74, 4, 1109-1132, (2006) · Zbl 1152.91428
[3] Chung, K.-S.; Olszewski, W., A non-differentiable approach to revenue equivalence, Theoretical econ., 2, 4, 469-487, (2007)
[4] Clarke, E.H., Multipart pricing of public goods, Public choice, 11, 1, 17-33, (1971)
[5] Ely, J.C., 2001. Revenue equivalence without differentiability assumptions. Mimeo: Department of Economics, Northwestern University
[6] Friedman, B., A note on convex functions, Bull. amer. math. soc., 46, 6, 473-474, (1940) · JFM 66.0243.02
[7] Groves, T., Incentives in teams, Econometrica, 41, 4, 617-631, (1973) · Zbl 0311.90002
[8] Heydenreich, B., Müller, R., Uetz, M., Vohra, R., 2008. Characterization of revenue equivalence. Mimeo: Department of Quantitative Economics, Maastricht University · Zbl 1160.91343
[9] Heydenreich, B.; Müller, R.; Uetz, M.; Vohra, R., Characterization of revenue equivalence, Econometrica, 77, 1, 307-316, (2009) · Zbl 1160.91343
[10] Holmström, B., Groves’ scheme on restricted domains, Econometrica, 47, 5, 1137-1144, (1979) · Zbl 0411.90004
[11] Jehiel, P.; Moldovanu, B., Efficient design with interdependent valuations, Econometrica, 69, 5, 1237-1259, (2001) · Zbl 1055.91517
[12] Jehiel, P.; Meyer-ter-Vehn, M.; Moldovanu, B.; Zame, W.R., The limits of ex post implementation, Econometrica, 74, 3, 585-610, (2006) · Zbl 1127.91046
[13] Krishna, V.; Maenner, E., Convex potentials with an application to mechanism design, Econometrica, 69, 4, 1113-1119, (2001)
[14] Milgrom, P.R.; Segal, I., Envelope theorems for arbitrary choice sets, Econometrica, 70, 2, 583-601, (2002) · Zbl 1103.90400
[15] Myerson, R.B., Optimal auction design, Math. oper. res., 6, 1, 58-73, (1981) · Zbl 0496.90099
[16] Myerson, R.B., Multistage games with communication, Econometrica, 54, 2, 323-358, (1986) · Zbl 0599.90134
[17] Roberts, K., The characterization of implementable choice rules, (), Chapter 18 · Zbl 0429.90009
[18] Rockafellar, R.T., Convex analysis, (1970), Princeton University Press Princeton, NJ · Zbl 0229.90020
[19] Rockafellar, R.T., The theory of subgradients and its applications to optimization problems, Research and education in mathematics, (1981), Heldermann-Verlag Princeton, NJ · Zbl 0462.90052
[20] Suijs, J., On incentive compatibility and budget balancedness in public decision making, Rev. econ. design, 2, 1, 193-209, (1996)
[21] Vickrey, W., Counterspeculation, auctions, and competitive sealed tenders, J. finance, 16, 1, 8-37, (1961)
[22] Williams, S.R., A characterization of efficient, Bayesian incentive compatible mechanisms, Econ. theory, 14, 1, 155-180, (1999) · Zbl 0942.91063
[23] Ziemer, W.P., Weakly differentiable functions, Graduate texts in mathematics, (1989), Springer-Verlag New York, NY · Zbl 0177.08006
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