Updating toward the signal
研究了“向信号更新”这一性质,即代理人的后验期望介于先验均值和无偏信号实现之间,并给出了该性质成立的充分必要条件。
Modelers frequently assume (either implicitly or explicitly) that an agent’s posterior expectation of some variable lies between their prior mean and the realization of an unbiased signal of that variable. We call this property updating toward the signal (UTS). We show that if the prior and signal error densities are both symmetric and quasiconcave then UTS will occur. If, for a given prior, UTS occurs for all symmetric and quasiconcave error densities, then in fact the prior must be symmetric and quasiconcave. Similar characterizations are derived for two additional updating requirements that are strictly weaker than UTS.