Memory Limitation and Multistage Decision Processes

Sequential decision models have heretofore assumed a full memory decision maker. That is, the model is permitted to retain, to any degree of precision, all information needed to optimize decision performance. This information may include functions or variables that change with observations and thus often implies a decision maker which possesses a large amount of soft (erasable) memory. In simple multistage decision problems soft memory can be reduced to two variables-the log-odds ratio L and the available number of observations n. The log-odds ratio is a quantitative measure of the decision maker's opinion of the cause of the observed variate. This paper examines the effect of limiting the decision maker's soft memory by specifying an m-bit register for the random variable L. The theory for limited memory multistage decision processes is presented in which there are two simple hypotheses. Numerical results indicate that the 3-bit memory is, for practical purposes, equivalent to a full memory decision maker.