The Law of Large Demand for Information
在廉价信息假设下,利用大偏差理论,解决了贝叶斯决策理论中信息的定价与估值问题,发现额外信号的边际价值随数量指数下降,且低质量信号边际价值更高。
An unresolved problem in Bayesian decision theory is how to value and price information. This paper resolves both problems assuming inexpensive information. Building on Large Deviation Theory, we produce a generically complete asymptotic order on samples of i.i.d. signals in finite–state, finite–action models. Computing the marginal value of an additional signal, we find it is eventually exponentially falling in quantity, and higher for lower quality signals. We provide a precise formula for the information demand, valid at low prices: asymptotically a constant times the log price, and falling in the signal quality for a given price.