Weak Monotonicity and Bayes-Nash Incentive Compatibility

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Weak Monotonicity and Bayes-Nash Incentive Compatibility

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Müller,Rudolf
Perea,Andrés
Wolf,Sascha (METEOR)

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Rudolf Müller

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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Paper provided by Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization in its series Research Memoranda with number 039.

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Date of creation: 2005
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Handle: RePEc:dgr:umamet:2005039

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Article
- Muller, Rudolf & Perea, Andres & Wolf, Sascha, 2007. "Weak monotonicity and Bayes-Nash incentive compatibility," Games and Economic Behavior, Elsevier, vol. 61(2), pages 344-358, November. [Downloadable!] (restricted)

This paper has been announced in the following NEP Reports:

NEP-ALL-2005-10-29 (All new papers)
NEP-GTH-2005-10-29 (Game Theory)
NEP-MIC-2005-10-29 (Microeconomics)
NEP-NET-2005-10-29 (Network Economics)

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

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. [Downloadable!]
Sushil Bikhchandani & Shurojit Chatterjee & Arunava Sen, 2004. "Incentive Compatibility in Multi-unit Auctions," Levine's Bibliography 122247000000000750, UCLA Department of Economics. [Downloadable!]
Gui,Hongwei & Müller,Rudolf & Vohra,Rakesh, 2004. "Dominant Strategy Mechanisms with Multidimensional Types," Research Memoranda 047, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Other versions:
- 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. [Downloadable!]
Klemperer, P., 1999. "Auction Theory: a Guide to the Literature," Economics Papers 1999-w12, Economics Group, Nuffield College, University of Oxford.
Other versions:
- Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Microeconomics 9903002, EconWPA. [Downloadable!]
- Klemperer, Paul, 1999. "Auction Theory: a Guide to the Literature," CEPR Discussion Papers 2163, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
- Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Blackwell Publishing, vol. 13(3), pages 227-86, July. [Downloadable!] (restricted)
Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
Jehiel, Philippe & Moldovanu, Benny & Stacchetti, Ennio, 1999. "Multidimensional Mechanism Design for Auctions with Externalities," Journal of Economic Theory, Elsevier, vol. 85(2), pages 258-293, April. [Downloadable!] (restricted)
Other versions:
- 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.
Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-59, September.
Other versions:
- Jehiel, Phillipe & Moldovanu, Benny, 1998. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 98-22, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim.
- Jehiel, Phillipe & Moldovanu, Benny, 1999. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 99-74, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
- Philippe Jehiel & Benny Moldovanu, 1998. "Efficient Design with Interdependent Valuations," Discussion Papers 1244, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]

Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

First:Birgit Heydenreich & Rudolf Muller & Marc Uetz & Rakesh Vohra, 2007. "Characterization of Revenue Equivalence," Discussion Papers 1448, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
Other versions:
- Müller Rudolf & Uetz Marc & Vohra Rakesh & Heydenreich Birgit, 2007. "Characterization of Revenue Equivalence," Research Memoranda 017, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
- Heydenreich Birgit & Müller Rudolf & Uetz Marc & Vohra Rakesh, 2008. "Characterization of Revenue Equivalence," Research Memoranda 001, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]
Müller Rudolf & Perea Andrés & Wolf Sascha, 2007. "Combinatorial Scoring Auctions," Research Memoranda 020, Maastricht : METEOR, Maastricht Research School of Economics of Technology and Organization. [Downloadable!]

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