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Alternatives to truthfulness are hard to recognize

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Abstract

The central question in mechanism design is how to implement a given social choice function. One of the most studied concepts is that of truthful implementations in which truth-telling is always the best response of the players. The Revelation Principle says that one can focus on truthful implementations without loss of generality (if there is no truthful implementation then there is no implementation at all). Green and Laffont (Rev Econ Stud 53:447–456, 1986) showed that, in the scenario in which players’ responses can be partially verified, the revelation principle holds only in some particular cases. When the Revelation Principle does not hold, non-truthful implementations become interesting since they might be the only way to implement a social choice function of interest. In this work we show that, although non-truthful implementations may exist, they are hard to find. Namely, it is NP-complete to decide if a given social choice function can be implemented in a non-truthful manner, or even if it can be implemented at all. This is in contrast to the fact that truthful implementability can be efficiently recognized, even when partial verification of the agents is allowed. Our results also show that there is no “simple” characterization of those social choice functions for which it is worth looking for non-truthful implementations.

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Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Università di Salerno, Salerno, Italy

    Vincenzo Auletta, Paolo Penna & Giuseppe Persiano

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Carmine Ventre

Authors
  1. Vincenzo Auletta
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  2. Paolo Penna
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  3. Giuseppe Persiano
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  4. Carmine Ventre
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Corresponding author

Correspondence to Carmine Ventre.

Additional information

A preliminary version of this paper is published in the Proceedings of the First International Symposium on Algorithmic Game Theory (Burkhard Monien, Ulf-Peter Schroeder (Eds.), Lecture Notes in Computer Science 4997 Springer 2008, pp. 194-205). Some of the results discussed in this paper have also been presented and included in the not formally published proceedings (only distributed as a bound volume) of the 2nd International Workshop on Computational Social Choice (COMSOC 2008).

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Auletta, V., Penna, P., Persiano, G. et al. Alternatives to truthfulness are hard to recognize. Auton Agent Multi-Agent Syst 22, 200–216 (2011). https://doi.org/10.1007/s10458-009-9119-4

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  • DOI: https://doi.org/10.1007/s10458-009-9119-4

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