Betting on the Real Line

  • Xi Gao
  • Yiling Chen
  • David M. Pennock
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5929)

Abstract

We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mechanisms, logarithmic market scoring rule (LMSR) and dynamic parimutuel markets (DPM), are generalized to handle interval bets on continuous or countably infinite outcomes. We examine problems associated with operating these markets. We show that the auctioneer’s order matching problem for interval bets can be solved in polynomial time for call markets. DPM can be generalized to deal with interval bets on both countably infinite and continuous outcomes and remains to have bounded loss. However, in a continuous-outcome DPM, a trader may incur loss even if the true outcome is within her betting interval. The LMSR market maker suffers from unbounded loss for both countably infinite and continuous outcomes.

Keywords

Prediction Markets Combinatorial Prediction Markets Expressive Betting 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Berg, J.E., Forsythe, R., Nelson, F.D., Rietz, T.A.: Results from a dozen years of election futures markets research. In: Plott, C.A., Smith, V. (eds.) Handbook of Experimental Economic Results (2001)Google Scholar
  2. 2.
    Wolfers, J., Zitzewitz, E.: Prediction markets. Journal of Economic Perspective 18(2), 107–126 (2004)CrossRefGoogle Scholar
  3. 3.
    Chen, K.Y., Plott, C.R.: Information aggregation mechanisms: Concept, design and implementation for a sales forecasting problem. Working paper No. 1131, California Institute of Technology (2002)Google Scholar
  4. 4.
    Hanson, R.D.: Combinatorial information market design. Information Systems Frontiers 5(1), 107–119 (2003)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Pennock, D.M.: A dynamic pari-mutuel market for hedging, wagering, and information aggregation. In: ACM Conference on Electronic Commerce, EC (2004)Google Scholar
  6. 6.
    Mangold, B., Dooley, M., Dornfest, R., Flake, G.W., Hoffman, H., Kasturi, T., Pennock, D.M.: The tech buzz game. IEEE Computer 38(7), 94–97 (2005)Google Scholar
  7. 7.
    Chen, Y., Fortnow, L., Nikolova, E., Pennock, D.M.: Betting on permutations. In: ACM Conference on Electronic Commerce (EC), pp. 326–335 (2007)Google Scholar
  8. 8.
    Ghodsi, M., Mahini, H., Mirrokni, V.S., ZadiMoghaddam, M.: Permutation betting markets: singleton betting with extra information. In: ACM Conference on Electronic Commerce (EC), pp. 180–189 (2008)Google Scholar
  9. 9.
    Agrawal, S., Wang, Z., Ye, Y.: Parimutuel betting on permutations. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 126–137. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  10. 10.
    Fortnow, L., Kilian, J., Pennock, D.M., Wellman, M.P.: Betting boolean-style: A framework for trading in securities based on logical formulas. Decision Support Systems 39(1), 87–104 (2004)Google Scholar
  11. 11.
    Chen, Y., Fortnow, L., Lambert, N., Pennock, D.M., Wortman, J.: Complexity of combinatorial market makers. In: ACM Conference on Electronic Commerce (EC), pp. 190–199 (2008)Google Scholar
  12. 12.
    Chen, Y., Goel, S., Pennock, D.M.: Pricing combinatorial markets for tournaments. In: ACM Symposium on Theory of Computing (STOC), pp. 305–314 (2008)Google Scholar
  13. 13.
    Goel, S., Pennock, D., Reeves, D.M., Yu, C.: Yoopick: A combinatorial sports prediction market. In: AAAI, pp. 1880–1881 (2008)Google Scholar
  14. 14.
    Agrawal, S., Delage, E., Peters, M., Wang, Z., Ye, Y.: A unified framework for dynamic pari-mutuel information market design. In: ACM Conference on Electronic Commerce (EC), pp. 255–264 (2009)Google Scholar
  15. 15.
    Bossaerts, P., Fine, L., Ledyard, J.: Inducing liquidity in thin financial markets through combined-value trading mechanisms. European Economic Review (46), 1671–1695 (2002)Google Scholar
  16. 16.
    Lange, J., Economides, N.: A parimutuel market microstructure for contingent claims trading. NYU School of Business Discussion Paper No. EC-01-13 (2007)Google Scholar
  17. 17.
    Baron, K., Lange, J.: Parimutuel Applications in Finance: New Markets for New Risks. Palgrave Macmillan, Basingstoke (2005)Google Scholar
  18. 18.
    Peters, M., So, A.M.C., Ye, Y.: Pari-mutuel markets: Mechanisms and performance. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 82–95. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Hanson, R.D.: Logarithmic market scoring rules for modular combinatorial information aggregation. Journal of Prediction Markets 1(1), 1–15 (2007)Google Scholar
  20. 20.
    Chen, Y., Pennock, D.M.: A utility framework for bounded-loss market makers. In: Conference on Uncertainty in Artificial Intelligence (UAI 2007), pp. 49–56 (2007)Google Scholar
  21. 21.
    Milgrom, P., Stokey, N.L.: Information, trade and common knowledge. Journal of Economic Theory 26(1), 17–27 (1982)MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Xi Gao
    • 1
  • Yiling Chen
    • 1
  • David M. Pennock
    • 2
  1. 1.Harvard University 
  2. 2.Yahoo! Research 

Personalised recommendations