If traders in prediction markets have state-dependent preferences so that marginal utility of money varies across states, prices in a rational expectation equilibrium are quantile statistics of distributions that derive from both distribution of realized signals and the distribution of state-dependence parameters. As a result, even with a common prior and regardless of whether prices reveal realized signals fully or not, the interpretation of prices as posterior probabilities remains problematic.
AllenB.JordanJ. S. (1998). The existence of rational expectations equilibrium: A retrospective. In Mukul Majumdar (ed.), Organizations with Incomplete Information, (pp. 42–60). Cambridge University Press.
2.
ArrowK. J.ForsytheR.GorhamM.HahnR.HansonR.LedyardJ. O.NelsonF. D. (2008). Economics: The promise of prediction markets. Science, 320(5878), 877. ISSN 0036–8075.
3.
BiaisB.GlostenL.SpattC. (2005). Market microstructure: A survey of microfoundations, empirical results, and policy implications. Journal of Financial Markets, 8(2), 217–264.
4.
HayekF. A. (1945). The use of knowledge in society. The American Economic Review, 35(4), 519–530.
5.
KarniE.SchmeidlerD. (2016). An expected utility theory for state-dependent preferences. Theory and Decision, 1–12.
6.
KyleA. S. (1985). Continuous auctions and insider trading. Econometrica: Journal of the Econometric Society, 53(6), 1315–1335.
7.
LieliR. P.Nieto-BarthaburuA. (2009). Feedback in prediction markets (Technical report). In Gabor Kezdi (ed.), Incentives, Predictions, Volumes, Prices. Essays commemorating the 20th anniversary of the first graduating class at CEU Economics. Budapest: Central European University Press.
8.
ManskiC. F. (2006). Interpreting the predictions of prediction markets. Economics Letters, 91(3), 425–429.
9.
MilgromP.StokeyN. (1982). Information, trade and common knowledge. Journal of Economic Theory, 26(1), 7–27.
10.
MorrisS. (1994). Trade with heterogeneous prior beliefs and asymmetric information. Econometrica: Journal of the Econometric Society, 62(6), 1327–1347
11.
O'haraM. (1995). Market microstructure theory (Vol.108). Cambridge, MA: Blackwell.
12.
OttavianiM.SørensenP. N. (2007). Outcome manipulation in corporate prediction markets. Journal of the European Economic Association, 5(2-3), 554–563.
13.
OttavianiM.SørensenP. N.. (2015). Price reaction to information with heterogeneous beliefs and wealth effects: Underreaction, momentum, and reversal. American Economic Review, 105(1), 1–34.
14.
RadnerR. (1979). Rational expectations equilibrium: Generic existence and the information revealed by prices. Econometrica: Journal of the Econometric Society, 47(3), 655–678.
15.
WolfersJ.ZitzewitzE. (2006). Interpreting prediction market prices as probabilities (Technical report). NBER Working Paper No. 12200 (May 2006). DOI: 10.3386/w12200. National Bureau of Economic Research.