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Weak monotonicity and Bayes-Nash incentive compatibility

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  • Muller, Rudolf
  • Perea, Andres
  • Wolf, Sascha

Abstract

An allocation rule is called Bayes-Nash incentive compatible, if there exists a payment rule, such that truthful reports of agents’ types form a Bayes-Nash equilibrium in the directrevelation mechanism consisting of the allocation rule and the payment rule. This paperprovides characterizations of Bayes-Nash incentive compatible allocation rules in socialchoice settings where agents have one-dimensional or multi-dimensional types, quasi-linearutility functions and interdependent valuations. The characterizations are derived byconstructing complete directed graphs on agents’ type spaces with cost of manipulationas lengths of edges. Weak monotonicity of the allocation rule corresponds to the conditionthat all 2-cycles in these graphs have non-negative length.For one-dimensional types and agents’ valuation functions satisfying non-decreasingexpected differences, we show that weak monotonicity of the allocation rule is a necessaryand sufficient condition for the rule to be Bayes-Nash incentive compatibile. In the casewhere types are multi-dimensional and the valuation for each outcome is a linear functionin the agent’s type, we show that weak monotonicity of the allocation rule together withan integrability condition is a necessary and sufficient condition for Bayes-Nash incentivecompatibility.

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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 61 (2007)
Issue (Month): 2 (November)
Pages: 344-358

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Handle: RePEc:eee:gamebe:v:61:y:2007:i:2:p:344-358

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Web page: http://www.elsevier.com/locate/inca/622836

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  1. Jehiel, Phillipe & Moldovanu, Benny & Stacchetti, E., 1997. "Multidimensional Mechanism Design for Auctions with Externalities," Sonderforschungsbereich 504 Publications 97-04, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
  2. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Economics Series Working Papers 1999-W12, University of Oxford, Department of Economics.
  3. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
  4. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  5. Hongwei Gui & Rudolf M¨uller & Rakesh V. Vohra, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Discussion Papers 1392, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. Philippe Jehiel & Benny Moldovanu, 1998. "Efficient Design with Interdependent Valuations," Discussion Papers 1244, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  7. Alexey Malakhov & Rakesh V. Vohra, 2004. "Single and Multi-Dimensional Optimal Auctions - A Network Approach," Discussion Papers 1397, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Birgit Heydenreich & Rudolf Müller & Marc Uetz & Rakesh V. Vohra, 2009. "Characterization of Revenue Equivalence," Econometrica, Econometric Society, vol. 77(1), pages 307-316, 01.
  2. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, 01.
  3. Debasis Mishra & Souvik Roy, 2011. "Implementation in multidimensional dichotomous domains," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 11-15, Indian Statistical Institute, New Delhi, India.
  4. Berger André & Müller Rudolf & Naeemi Seyed Hossein, 2010. "Path-Monotonicity and Incentive Compatibility," Research Memorandum 035, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  5. Heydenreich, Birgit & Mishra, Debasis & Müller, Rudolf & Uetz, Marc, 2008. "Optimal Mechanisms for Single Machine Scheduling," Research Memorandum 033, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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