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A Network Approach to Bayes-Nash Incentive Compatible Mechanisms

Authors: Rudolf Müller, Andres Perea, and Sascha Wolf

Published in: Dagstuhl Seminar Proceedings, Volume 5011, Computing and Markets (2005)

Abstract

This paper provides a characterization of Bayes-Nash incentive compatible mechanisms in settings where agents have one-dimensional or multi-dimensional types, quasi-linear utility functions and interdependent valuations. The characterization is derived in terms of conditions for the underlying allocation function. We do this by making a link to network theory and building complete directed graphs for agents type spaces. We show that an allocation rule is Bayes-Nash incentive compatible if and only if these graphs have no negative, finite cycles. In the case of one-dimensional types and given certain properties for agents valuation functions, we show that this condition reduces to the absence of negative 2-cycles. In the case of multi-dimensional types and given a linearity requirement on the valuation functions, we show that this condition reduces to the absence of negative 2-cycles and an integratebility condition on the valuation functions.

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Rudolf Müller, Andres Perea, and Sascha Wolf. A Network Approach to Bayes-Nash Incentive Compatible Mechanisms. In Computing and Markets. Dagstuhl Seminar Proceedings, Volume 5011, pp. 1-10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2005)

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@InProceedings{muller_et_al:DagSemProc.05011.4,
  author =	{M\"{u}ller, Rudolf and Perea, Andres and Wolf, Sascha},
  title =	{{A Network Approach to Bayes-Nash Incentive Compatible Mechanisms}},
  booktitle =	{Computing and Markets},
  pages =	{1--10},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2005},
  volume =	{5011},
  editor =	{Daniel Lehmann and Rudolf M\"{u}ller and Tuomas Sandholm},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.05011.4},
  URN =		{urn:nbn:de:0030-drops-2056},
  doi =		{10.4230/DagSemProc.05011.4},
  annote =	{Keywords: compact representation of games, congestion games, local-effect games, action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio}
}

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A Network Approach to Bayes-Nash Incentive Compatible Mechanisms

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