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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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Suggested Citation

  • 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.
  • Handle: RePEc:eee:gamebe:v:61:y:2007:i:2:p:344-358
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    1. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, vol. 69(5), pages 1237-1259, September.
    2. 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.
    3. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-286, July.
    4. Sushil Bikhchandani & Shurojit Chatterji & Ron Lavi & Ahuva Mu'alem & Noam Nisan & Arunava Sen, 2006. "Weak Monotonicity Characterizes Deterministic Dominant-Strategy Implementation," Econometrica, Econometric Society, vol. 74(4), pages 1109-1132, July.
    5. Krishna, Vijay & Maenner, Eliot, 2001. "Convex Potentials with an Application to Mechanism Design," Econometrica, Econometric Society, vol. 69(4), pages 1113-1119, July.
    6. Klemperer, Paul, 1999. " Auction Theory: A Guide to the Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 13(3), pages 227-86, July.
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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, January.
    2. André Berger & Rudolf Müller & Seyed Hossein Naeemi, 2017. "Characterizing implementable allocation rules in multi-dimensional environments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(2), pages 367-383, February.
    3. 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.
    4. 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, January.
    5. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2014. "Multidimensional mechanism design in single peaked type spaces," Journal of Economic Theory, Elsevier, vol. 153(C), pages 103-116.
    6. Mishra, Debasis & Roy, Souvik, 2013. "Implementation in multidimensional dichotomous domains," Theoretical Economics, Econometric Society, vol. 8(2), May.
    7. 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).
    8. 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).
    9. Tomoya Kazumura & Debasis Mishra & Shigehiro Serizawa, 2017. "Mechanism design without quasilinearity," ISER Discussion Paper 1005, Institute of Social and Economic Research, Osaka University.

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