State-dependent Preferences in Prediction Markets and Prices as Aggregate Statistic

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 the 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.