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Unrestricted Domain Extensions of Dominant Strategy Implementable Allocation Functions

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Social Design

Part of the book series: Studies in Economic Design ((DESI))

Abstract

It is shown that any one-person dominant strategy implementable allocation function on a restricted domain of types can be extended to the unrestricted domain in such a way that dominant strategy implementability is preserved when utility is quasilinear. A sufficient condition is identified for which this extension is essentially unique.

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Notes

  1. 1.

    The main results in Gui et al. (2004) also appear in Vohra (2011).

  2. 2.

    Further details about the material discussed in Sects. 2–5 and 9 may be found in Edelman and Weymark (2017), Heydenreich et al. (2009), and Vohra (2011).

  3. 3.

    In Figs. 2 and 3, we do not label these three normalized difference sets. However, they are easily identified by our descriptions of their construction.

References

  • Cuff, K., Hong, S., Schwartz, J. A., Wen, Q., & Weymark, J. A. (2012). Dominant strategy implementation with a convex product set of valuations. Social Choice and Welfare, 39, 567–597.

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  • Edelman, P. H., & Weymark, J. A. (2017). Dominant Strategy Implementability and Zero Length Cycles. Working paper No. 2972177, SSRN.

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  • Gui, H., Müller, R., & Vohra, R. V. (2004). Characterizing Dominant Strategy Mechanisms with Multi-Dimensional Types. Discussion Paper No. 1392, Center for Mathematical Studies in Economics and Management Science, Northwestern University.

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  • Heydenreich, B., Müller, R., Uetz, M., & Vohra, R. V. (2009). Characterization of revenue equivalence. Econometrica, 77, 307–316.

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  • Rochet, J. C. (1987). A necessary and sufficient condition for rationalizability in a quasi-linear context. Journal of Mathematical Economics, 16, 191–200.

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  • Vohra, R. V. (2011). Mechanism design: A linear programming approach. Cambridge: Cambridge University Press.

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Acknowledgements

We are grateful to a referee of Edelman and Weymark (2017) for suggesting the argument used in the first proof of Theorem 6. We are also grateful to Alexey Kushnir for a conversation about unrestricted domain extensions and to Walter Trockel for comments on a previous draft.

Author information

Authors and Affiliations

  1. Department of Mathematics and the Law School, Vanderbilt University, Nashville, TN, USA

    Paul H. Edelman

  2. Department of Economics, Vanderbilt University, Nashville, TN, USA

    John A. Weymark

Authors
  1. Paul H. Edelman
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  2. John A. Weymark
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Corresponding author

Correspondence to John A. Weymark .

Editor information

Editors and Affiliations

  1. Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    Walter Trockel

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Edelman, P.H., Weymark, J.A. (2019). Unrestricted Domain Extensions of Dominant Strategy Implementable Allocation Functions. In: Trockel, W. (eds) Social Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-319-93809-7_16

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