Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This is a slight departure from the formalization of the game in [18]. There, Alice did not automatically observe Bob’s signal, causing complications in the case where Bob’s report \(\mathbf {p}_{S,B}\) could be the same for two different outcomes \(b,b' \in \mathcal {B}\).
- 2.
Such a signaling scheme is also called an experiment by Kolotilin et al. [17]. We remark that their model is a special case of the general model we described here, with independent A, B and binary receiver actions.
- 3.
Note that if \(\lambda > 1\) in the \(\lambda \)-nice condition, or if \(\beta > 1\) in the \((\alpha ,\beta )\)-local Hölder continuity condition, then G is identically zero so we are not interested in those trivial cases.
References
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)
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)
Bergemann, D., Morris, S.: The comparison of information structures in games: Bayes correlated equilibrium and individual sufficiency. Technical report 2, May 2016
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)
Chen, Y., et al.: Gaming prediction markets: equilibrium strategies with a market maker. Algorithmica 58(4), 930–969 (2010)
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). https://doi.org/10.1007/978-3-540-77105-0_10
Chen, Y., Waggoner, B.: Informational substitutes. In: 56th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2016 (2016)
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)
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)
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)
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). https://doi.org/10.1145/2482540.2482592
Gneiting, T., Raftery, A.E.: Strictly proper scoring rules, prediction, and estimation. J. Am. Stat. Assoc. 102(477), 359–378 (2007)
Hanson, R.: Combinatorial information market design. Inf. Syst. Front. 5(1), 107–119 (2003)
Howard, R.A.: Information value theory. IEEE Trans. Syst. Sci. Cybern. 2(1), 22–26 (1966)
Iyer, K., Johari, R., Moallemi, C.C.: Information aggregation and allocative efficiency in smooth markets. Manag. Sci. 60(10), 2509–2524 (2014)
Kamenica, E., Gentzkow, M.: Bayesian persuasion. Am. Econ. Rev. 101(6), 2590–2615 (2011)
Kolotilin, A., Mylovanov, T., Zapechelnyuk, A., Li, M.: Persuasion of a privately informed receiver. Econometrica 85(6), 1949–1964 (2017)
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)
Lambert, N.S., et al.: An axiomatic characterization of wagering mechanisms. J. Econ. Theory 156, 389–416 (2014)
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)
McCarthy, J.: Measures of the value of information. Proc. Nat. Acad. Sci. 42(9), 654–655 (1956)
Ostrovsky, M.: Information aggregation in dynamic markets with strategic traders. Econometrica 80(6), 2595–2647 (2012)
Savage, L.J.: Elicitation of personal probabilities and expectations. J. Am. Stat. Assoc. 66(336), 783–801 (1971)
Tetlock, P.E., Gardner, D.: Superforecasting: The Art and Science of Prediction. Broadway Books, New York (2016)
Witkowski, J., Freeman, R., Vaughan, J.W., Pennock, D.M., Krause, A.: Incentive-compatible forecasting competitions. In: AAAI (2018)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Anunrojwong, J., Chen, Y., Waggoner, B., Xu, H. (2019). Computing Equilibria of Prediction Markets via Persuasion. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-35389-6_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35388-9
Online ISBN: 978-3-030-35389-6
eBook Packages: Computer ScienceComputer Science (R0)