Computing Equilibria of Prediction Markets via Persuasion

  • Jerry AnunrojwongEmail author
  • Yiling Chen
  • Bo Waggoner
  • Haifeng Xu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11920)


We study the computation of equilibria in prediction markets in perhaps the most fundamental special case with two players and three trading opportunities. To do so, we show equivalence of prediction market equilibria with those of a simpler signaling game with commitment introduced by Kong and Schoenebeck [18]. We then extend their results by giving computationally efficient algorithms for additional parameter regimes. Our approach leverages a new connection between prediction markets and Bayesian persuasion, which also reveals interesting conceptual insights.


  1. 1.
    Abernethy, J., Chen, Y., Vaughan, J.W.: Efficient market making via convex optimization, and a connection to online learning. ACM Trans. Econ. Comput. 1(2), 12 (2013) CrossRefGoogle Scholar
  2. 2.
    Berg, J., Forsythe, R., Nelson, F., Rietz, T.: Results from a dozen years of election futures markets research. In: Handbook of Experimental Economics Results (2008)CrossRefGoogle Scholar
  3. 3.
    Bergemann, D., Morris, S.: The comparison of information structures in games: Bayes correlated equilibrium and individual sufficiency. Technical report 2, May 2016Google Scholar
  4. 4.
    Bhaskar, U., Cheng, Y., Ko, Y.K., Swamy, C.: Hardness results for signaling in Bayesian zero-sum and network routing games. In: Proceedings of the 2016 ACM Conference on Economics and Computation, pp. 479–496. ACM (2016)Google Scholar
  5. 5.
    Chen, Y., et al.: Gaming prediction markets: equilibrium strategies with a market maker. Algorithmica 58(4), 930–969 (2010)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chen, Y., Reeves, D.M., Pennock, D.M., Hanson, R.D., Fortnow, L., Gonen, R.: Bluffing and strategic reticence in prediction markets. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 70–81. Springer, Heidelberg (2007). Scholar
  7. 7.
    Chen, Y., Waggoner, B.: Informational substitutes. In: 56th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 (2016)Google Scholar
  8. 8.
    Cheng, Y., Cheung, H.Y., Dughmi, S., Emamjomeh-Zadeh, E., Han, L., Teng, S.H.: Mixture selection, mechanism design, and signaling. In: 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, pp. 1426–1445. IEEE (2015)Google Scholar
  9. 9.
    Dimitrov, S., Sami, R.: Non-myopic strategies in prediction markets. In: Proceedings of the 9th ACM Conference on Electronic Commerce, EC 2008, pp. 200–209. ACM (2008)Google Scholar
  10. 10.
    Freeman, R., Pennock, D.M., Vaughan, J.W.: The double clinching auction for wagering. In: Proceedings of the 18th Conference on Economics and Computation (EC) (2017)Google Scholar
  11. 11.
    Gao, X.A., Zhang, J., Chen, Y.: What you jointly know determines how you act: strategic interactions in prediction markets. In: Proceedings of the 14th ACM Conference on Electronic Commerce, EC 2013, pp. 489–506. ACM (2013).
  12. 12.
    Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102(477), 359–378 (2007)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Hanson, R.: Combinatorial information market design. Inf. Syst. Front. 5(1), 107–119 (2003)CrossRefGoogle Scholar
  14. 14.
    Howard, R.A.: Information value theory. IEEE Trans. Syst. Sci. Cybern. 2(1), 22–26 (1966)CrossRefGoogle Scholar
  15. 15.
    Iyer, K., Johari, R., Moallemi, C.C.: Information aggregation and allocative efficiency in smooth markets. Manag. Sci. 60(10), 2509–2524 (2014)CrossRefGoogle Scholar
  16. 16.
    Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101(6), 2590–2615 (2011)CrossRefGoogle Scholar
  17. 17.
    Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Kong, Y., Schoenebeck, G.: Optimizing Bayesian information revelation strategy in prediction markets: the Alice Bob Alice case. In: 9th Innovations in Theoretical Computer Science Conference, ITCS 2018 (2018)Google Scholar
  19. 19.
    Lambert, N.S., et al.: An axiomatic characterization of wagering mechanisms. J. Econ. Theory 156, 389–416 (2014)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Lambert, N.S., et al.: Self-financed wagering mechanisms for forecasting. In: Proceedings of the 9th ACM Conference on Electronic Commerce, EC 2008, pp. 170–179. ACM (2008)Google Scholar
  21. 21.
    McCarthy, J.: Measures of the value of information. Proc. Nat. Acad. Sci. 42(9), 654–655 (1956)CrossRefGoogle Scholar
  22. 22.
    Ostrovsky, M.: Information aggregation in dynamic markets with strategic traders. Econometrica 80(6), 2595–2647 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Savage, L.J.: Elicitation of personal probabilities and expectations. J. Am. Stat. Assoc. 66(336), 783–801 (1971)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Tetlock, P.E., Gardner, D.: Superforecasting: The Art and Science of Prediction. Broadway Books, New York (2016)Google Scholar
  25. 25.
    Witkowski, J., Freeman, R., Vaughan, J.W., Pennock, D.M., Krause, A.: Incentive-compatible forecasting competitions. In: AAAI (2018)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Jerry Anunrojwong
    • 1
    • 2
    Email author
  • Yiling Chen
    • 3
  • Bo Waggoner
    • 4
  • Haifeng Xu
    • 3
    • 5
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.Chulalongkorn UniversityBangkokThailand
  3. 3.Harvard UniversityCambridgeUSA
  4. 4.University of Colorado BoulderBoulderUSA
  5. 5.University of VirginiaCharlottesvilleUSA

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