Abstract
Roberts (Aggregation and Revelation of Preferences. Papers presented at the 1st European Summer Workshop of the Econometric Society, pp. 321–349. North-Holland, 1979) showed that every social choice function that is ex-post implementable in private value settings must be weighted VCG, i.e. it maximizes the weighted social welfare. This paper provides two simplified proofs for this. The first proof uses the same underlying key-point, but significantly simplifies the technical construction around it, thus helps to shed light on it. The second proof builds on monotonicity conditions identified by Rochet (J Math Econ 16:191–200, 1987) and Bikhchandani et al. (Econometrica 74(4):1109–1132, 2006). This proof is for a weaker statement that assumes an additional condition of “player decisiveness”.
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References
Bartal Y, Gonen R, Nisan N (2003) Incentive compatible multi-unit combinatorial auctions, 2003. Working paper, The Hebrew University. Presented in TARK-03
Bikhchandani S, Chatterji S, Lavi R, Mu’alem A, Nisan N, Sen A (2006) Weak monotonicity characterizes deterministic dominant strategy implementation. Econometrica 74(4): 1109–1132
Gui H, Muller R, Vohra R (2004) Characterizing dominant strategy mechanisms with multi-dimensional types, 2004. Working paper, Northwestern University
Holzman R, Monderer D (2004) Characterization of ex-post equilibrium in the VCG combinatorial auctions. Games Econ Behav 47: 87–103
Jehiel P, ter Vehn MM, Moldovanu B (2004) Ex-post implementation and preference aggregation via potenials, 2004. Working paper (in revision for J Econ Theory)
Kalai E, Muller E, Satterthwaite M (1979) Social welfare functions when preferences are convex, strictly monotonic, and continuous. Public Choice 34: 87–97
Lavi R, Mu’alem A, Nisan N (2003) Towards a characterization of truthful combinatorial auctions, 2003. Working paper, The Hebrew University. Preliminary version presented in FOCS-03
Meyer-ter-Vehn M, Moldovanu B (2002) Ex-post implementation with interdependent valuations, 2002. Discussion paper, University of Bonn
Myerson R (1981) Optimal auction design. Math Oper Res 6: 58–73
Roberts K (1979) The characterization of implementable choice rules. In: Laffont J (ed) Aggregation and revelation of preferences. Papers presented at the 1st European Summer Workshop of the Econometric Society, pp 321–349, North-Holland
Rochet JC (1987) A necessary and sufficient condition for rationalizability in a quasi-linear context. J Math Econ 16: 191–200
Rozenshtrom I (1999) Dominant strategy implementation with quasi-linear preferences, 1999. Master’s thesis, Dept. of Economics, The Hebrew University, Jerusalem, Israel
Saks M, Yu L (2005) Weak monotonicity suffices for truthfulness on convex domains. In: Proceedings of the 7th ACM Conference on Electronic Commerce (ACM-EC)
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Supported by grants from the Israeli Ministry of Science and the Israeli Academy of Sciences.
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Lavi, R., Mu’alem, A. & Nisan, N. Two simplified proofs for Roberts’ theorem. Soc Choice Welf 32, 407–423 (2009). https://doi.org/10.1007/s00355-008-0331-y
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DOI: https://doi.org/10.1007/s00355-008-0331-y