Abstract
We study implementability in dominant strategies of social choice functions when sets of types are multi-dimensional and convex, sets of outcomes are arbitrary, valuations for outcomes are convex functions in the type, and utilities over outcomes and payments are quasi-linear. Archer and Kleinberg [1] have proven that in case of valuation functions that are linear in the type monotonicity in combination with a local integrability condition are equivalent with implementability. We show that in the case of convex valuation functions one has to require in addition a property called decomposition monotonicity in order to conclude implementability from monotonicity and the integrability condition. Decomposition monotonicity is automatically satisfied in the linear case.
Saks and Yu [9] have shown that for the same setting as in Archer and Kleinberg [1], but finite set of outcomes, monotonicity alone is sufficient for implementability. Later Archer and Kleinberg [1], Monderer [6] and Vohra [10] have given alternative proofs for the same theorem. Using our characterization, we show that the Saks and Yu theorem generalizes to convex valuations. Again, decomposition monotonicity has to be added as a condition.
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References
Archer, A., Kleinberg, R.: Truthful germs are contagious: a local to global characterization of truthfulness. In: EC 2008: Proceedings of the 9th ACM conference on Electronic commerce, pp. 21–30. ACM, New York (2008)
Gui, H., Müller, R., Vohra, R.: Dominant strategy mechanisms with multidimensional types. In: Discussion Paper 1392. The Center for Mathematical Studies in Economics & Management Sciences, Northwestern University, Evanston (2004)
Heydenreich, B., Müller, R., Uetz, M., Vohra, R.: Characterization of revenue equivalence. Econometrica 77, 307–316 (2009)
Jehiel, P., Moldovanu, B., Stacchetti, E.: Multidimensional mechanism design for auctions with externalities. Journal of Economic Theory 85(2), 258–293 (1999)
Krishna, V., Maenner, E.: Convex potentials with an application to mechanism design. Econometrica 69(4), 1113–1119 (2001)
Monderer, D.: Monotonicity and implementability: extended abstract. In: EC 2008: Proceedings of the 9th ACM conference on Electronic commerce, pp. 48–48. ACM, New York (2008)
Müller, R., Perea, A., Wolf, S.: Weak monotonicity and Bayes-Nash incentive compatibility. Games and Economic Behavior 61(2), 344–358 (2007)
Rochet, J.-C.: A necessary and sufficient condition for rationalizability in a quasi-linear context. Journal of Mathematical Economics 16(2), 191–200 (1987)
Saks, M., Yu, L.: Weak monotonicity suffices for truthfulness on convex domains. In: Proc. 6th ACM conference on Electronic Commerce, pp. 286–293 (2005)
Vohra, R.: Paths, cycles and mechanism design. Technical report, Northwestern University (2007)
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Berger, A., Müller, R., Naeemi, S.H. (2009). Characterizing Incentive Compatibility for Convex Valuations. In: Mavronicolas, M., Papadopoulou, V.G. (eds) Algorithmic Game Theory. SAGT 2009. Lecture Notes in Computer Science, vol 5814. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04645-2_4
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DOI: https://doi.org/10.1007/978-3-642-04645-2_4
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