Mixing Coins of Different Quality: A Game-Theoretic Approach

  • Svetlana AbramovaEmail author
  • Pascal Schöttle
  • Rainer Böhme
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10323)


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.


Bitcoin Anonymity Blacklisting Policy Game theory 



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.


  1. 1.
    Aceto, G., Pescapé, A.: Internet censorship detection: a survey. Comput. Netw. 83, 381–421 (2015)CrossRefGoogle Scholar
  2. 2.
    Acquisti, A., Dingledine, R., Syverson, P.: On the economics of anonymity. In: Wright, R.N. (ed.) FC 2003. LNCS, vol. 2742, pp. 84–102. Springer, Heidelberg (2003). CrossRefGoogle Scholar
  3. 3.
    Akerlof, G.A.: The market for “Lemon”: quality uncertainty and the market mechanism. Q. J. Econ. 84(3), 161–167 (1970)CrossRefGoogle Scholar
  4. 4.
    Androulaki, E., Karame, G.O., Roeschlin, M., Scherer, T., Capkun, S.: Evaluating user privacy in bitcoin. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 34–51. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  5. 5.
    blockCollector: Looking to buy an old 50 BTC block. Where to buy? (2015). Accessed 14 Nov 2016
  6. 6.
    Böhme, R., Christin, N., Edelman, B., Moore, T.: Bitcoin: economics, technology, and governance. J. Econ. Perspect. 29(2), 213–238 (2015)CrossRefGoogle Scholar
  7. 7.
    Bonneau, J., Miller, A., Clark, J., Narayanan, A., Kroll, J.A., Felten, E.W.: SoK: research perspectives and challenges for bitcoin and cryptocurrencies. In: Proceedings of IEEE Symposium on Security and Privacy, pp. 104–121 (2015)Google Scholar
  8. 8.
    Bonneau, J., Narayanan, A., Miller, A., Clark, J., Kroll, J.A., Felten, E.W.: Mixcoin: anonymity for bitcoin with accountable mixes. In: Christin, N., Safavi-Naini, R. (eds.) FC 2014. LNCS, vol. 8437, pp. 486–504. Springer, Heidelberg (2014). Google Scholar
  9. 9.
    Chacko, G., Jurek, J., Stafford, E.: The price of immediacy. J. Financ. 63(3), 1253–1290 (2008)CrossRefGoogle Scholar
  10. 10.
    Chaum, D.L.: Untraceable electronic mail, return addresses, and digital pseudonyms. Commun. ACM 24(2), 84–90 (1981)CrossRefGoogle Scholar
  11. 11.
    Edwards, B., Moore, T., Stelle, G., Hofmeyr, S., Forrest, S.: Beyond the blacklist: modeling malware spread and the effect of interventions. In: Proceedings of 2012 Workshop on New Security Paradigms, pp. 53–66. ACM, New York (2012)Google Scholar
  12. 12.
    ExpertNeeded: Blockchain analysis help needed. Major money laundering case. (2016). Accessed 14 Nov 2016
  13. 13.
    Henry, R., Goldberg, I.: Formalizing anonymous blacklisting systems. In: Proceedings of IEEE Symposium on Security and Privacy, pp. 81–95. IEEE Computer Society, Washington, DC (2011)Google Scholar
  14. 14.
    Hofmeyr, S., Moore, T., Forrest, S., Edwards, B., Stelle, G.: Modeling internet-scale policies for cleaning up malware. In: Schneier, B. (ed.) Economics of Information Security and Privacy III. LNCS, pp. 149–170. Springer, New York (2013). CrossRefGoogle Scholar
  15. 15.
    Meiklejohn, S., Orlandi, C.: Privacy-enhancing overlays in bitcoin. In: Brenner, M., Christin, N., Johnson, B., Rohloff, K. (eds.) FC 2015. LNCS, vol. 8976, pp. 127–141. Springer, Heidelberg (2015). CrossRefGoogle Scholar
  16. 16.
    Meiklejohn, S., Pomarole, M., Jordan, G., Levchenko, K., McCoy, D., Voelker, G.M., Savage, S.: A fistful of bitcoins: characterizing payments among men with no names. In: Proceedings of 2013 Conference on Internet Measurement Conference, pp. 127–140. ACM, New York (2013)Google Scholar
  17. 17.
    Möser, M., Böhme, R.: Join me on a market for anonymity. In: Proceedings of 15th Annual Workshop on the Economics of Information Security, Berkeley, CA, USA (2016)Google Scholar
  18. 18.
    Möser, M., Böhme, R.: Anonymous alone? Measuring bitcoin’s second-generation anonymization techniques. In: IEEE Security & Privacy on the Blockchain (IEEE S&B), Paris, France (2017)Google Scholar
  19. 19.
    Möser, M., Böhme, R., Breuker, D.: An inquiry into money laundering tools in the bitcoin ecosystem. In: APWG eCrime Researchers Summit (ECRIME), San Francisco, CA, USA, pp. 1–14 (2013)Google Scholar
  20. 20.
    Möser, M., Böhme, R., Breuker, D.: Towards risk scoring of bitcoin transactions. In: Böhme, R., Brenner, M., Moore, T., Smith, M. (eds.) FC 2014. LNCS, vol. 8438, pp. 16–32. Springer, Heidelberg (2014). Google Scholar
  21. 21.
    Nakamoto, S.: Bitcoin: a peer-to-peer electronic cash system (2008). Accessed 14 Nov 2016
  22. 22.
    Pfitzmann, A., Hansen, M.: Anonymity, unlinkability, unobservability, pseudonymity, and identity management - a consolidated proposal for terminology, Technical report (2005)Google Scholar
  23. 23.
    Reid, F., Harrigan, M.: An analysis of anonymity in the bitcoin system. In: Altshuler, Y., Elovici, Y., Cremers, B.A., Aharony, N., Pentland, A. (eds.) Security and Privacy in Social Networks, pp. 197–223. Springer, New York (2013)CrossRefGoogle Scholar
  24. 24.
    Ron, D., Shamir, A.: Quantitative analysis of the full bitcoin transaction graph. In: Sadeghi, A.-R. (ed.) FC 2013. LNCS, vol. 7859, pp. 6–24. Springer, Heidelberg (2013). CrossRefGoogle Scholar
  25. 25.
    Rosenfeld, M.: Overview of colored coins (2015). Accessed 14 Nov 2016
  26. 26.
    Sheng, S., Wardman, B., Warner, G., Cranor, L.F., Hong, J., Zhang, C.: An empirical analysis of phishing blacklists. In: Proceedings of 6th Conference on Email and Anti-Spam, CEAS 2009 (2009)Google Scholar
  27. 27.
    Siegel, D.: Understanding the DAO hack for journalists (2016). Accessed 14 Nov 2016
  28. 28.
    Spence, M.: Job market signaling. Q. J. Econ. 87(3), 355–374 (1973)CrossRefGoogle Scholar
  29. 29.
    Tadelis, S.: Game Theory: An Introduction. Princeton University Press, Princeton (2013)zbMATHGoogle Scholar
  30. 30.
    TraderSteve: Bitpay is blacklisting certain bitcoins & rejecting customers. (2015). Accessed 14 Nov 2016
  31. 31.
    Tsalis, N., Virvilis, N., Mylonas, A., Apostolopoulos, T., Gritzalis, D.: Browser blacklists: the utopia of phishing protection. In: Obaidat, M.S., Holzinger, A., Filipe, J. (eds.) ICETE 2014. CCIS, vol. 554, pp. 278–293. Springer, Cham (2015). CrossRefGoogle Scholar
  32. 32.
    Vasek, M., Weeden, M., Moore, T.: Measuring the impact of sharing abuse data with web hosting providers. In: Proceedings of 2016 ACM on Workshop on Information Sharing and Collaborative Security, WISCS 2016, pp. 71–80. ACM, New York (2016)Google Scholar
  33. 33.
    Yanovich, Y., Mischenko, P., Ostrovskiy, A.: Shared send untangling in bitcoin. In: Working Paper, Bitfury Group Limited (2016). Accessed 14 Nov 2016

Copyright information

© International Financial Cryptography Association 2017

Authors and Affiliations

  • Svetlana Abramova
    • 1
    • 2
    Email author
  • Pascal Schöttle
    • 1
  • Rainer Böhme
    • 1
    • 2
  1. 1.University of InnsbruckInnsbruckAustria
  2. 2.University of MünsterMünsterGermany

Personalised recommendations