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Weak Monotonicity and Bayes-Nash Incentive Compatibility

  • Müller Rudolf
  • Perea Andrés
  • Wolf Sascha

    (METEOR)

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 University, Maastricht Research School of Economics of Technology and Organization (METEOR) in its series Research Memorandum with number 039.

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Date of creation: 2005
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Handle: RePEc:unm:umamet:2005039
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  1. Jehiel, Phillipe & Moldovanu, Benny, 1998. "Efficient Design with Interdependent Valuations," Sonderforschungsbereich 504 Publications 98-22, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  2. 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.
  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. 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.
  5. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-19, July.
  6. Paul Klemperer, 1999. "Auction Theory: A Guide to the Literature," Economics Series Working Papers 1999-W12, University of Oxford, Department of Economics.
  7. 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.
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