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Mixing Coins of Different Quality: A Game-Theoretic Approach

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Financial Cryptography and Data Security (FC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10323))

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Abstract

Cryptocoins based on public distributed ledgers can differ in their quality due to different subjective values users assign to coins depending on the unique transaction history of each coin. We apply game theory to study how qualitative differentiation between coins will affect the behavior of users interested in improving their anonymity through mixing services. We present two stylized models of mixing with perfect and imperfect information and analyze them for three distinct quality propagation policies: poison, haircut, and seniority. In the game of perfect information, mixing coins of high quality remains feasible under certain conditions, while imperfect information eventually leads to a mixing market where only coins of the lowest quality are mixed.

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Notes

  1. 1.

    Otherwise, switch players A and B.

  2. 2.

    Note that the game of perfect information under the poison regime has even more Nash equilibria. However, these are not subgame perfect.

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Acknowledgments

The authors are grateful to Daniel G. Arce for his insightful comments on an earlier version of this paper. The authors are responsible for all remaining errors and omissions. This work was funded by the German Bundesministerium für Bildung und Forschung (BMBF) under grant agreement No. 13N13505 and by Archimedes Privatstiftung, Innsbruck, Austria.

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Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Svetlana Abramova, Pascal Schöttle & Rainer Böhme

  2. University of Münster, Münster, Germany

    Svetlana Abramova & Rainer Böhme

Authors
  1. Svetlana Abramova
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  2. Pascal Schöttle
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  3. Rainer Böhme
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Corresponding author

Correspondence to Svetlana Abramova .

Editor information

Editors and Affiliations

  1. Leibniz Universität Hannover, Hannover, Germany

    Michael Brenner

  2. New Jersey Institute of Technology, Newark, New Jersey, USA

    Kurt Rohloff

  3. New York University, New York, New York, USA

    Joseph Bonneau

  4. University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

    Andrew Miller

  5. University of Luxembourg, Luxembourg, Luxembourg

    Peter Y.A. Ryan

  6. University of Melbourne, Parkville, Victoria, Australia

    Vanessa Teague

  7. University of Stirling, Stirling, United Kingdom

    Andrea Bracciali

  8. University of Trento, Trento, Italy

    Massimiliano Sala

  9. University of Trento, Trento, Italy

    Federico Pintore

  10. Agari Inc., San Mateo, California, USA

    Markus Jakobsson

A Appendix

A Appendix

Fig. 4.
figure 4

Seniority policy: examples of mixing transactions in the perfect information regime: (a) shows the case when both coins are either good or bad (2 outputs); (b) – when both coins are of the same quality \(q \in (0,1)\) (4 outputs); (c) – when coins are of different quality (the number of outputs equals two times the least common divisor of the denominators of \(q_a\) and \(q_b\) expressed as rational numbers). The mixing fee is disregarded in these examples (\(c=0\)).

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Abramova, S., Schöttle, P., Böhme, R. (2017). Mixing Coins of Different Quality: A Game-Theoretic Approach. In: Brenner, M., et al. Financial Cryptography and Data Security. FC 2017. Lecture Notes in Computer Science(), vol 10323. Springer, Cham. https://doi.org/10.1007/978-3-319-70278-0_18

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  • DOI: https://doi.org/10.1007/978-3-319-70278-0_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70277-3

  • Online ISBN: 978-3-319-70278-0

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