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A Network Approach to Bayes-Nash Incentive Compatible Mechanisms

Authors Rudolf Müller, Andres Perea, Sascha Wolf



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Rudolf Müller
Andres Perea
Sascha Wolf

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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)
https://doi.org/10.4230/DagSemProc.05011.4

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.
Keywords
  • compact representation of games
  • congestion games
  • local-effect games
  • action-graph gamescomputational markets; auctions; bidding strategiesNegotiatio

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