Approximate evaluations of value functions with a large number of alternatives
Although the use of value functions is theoretically appealing, it is not easily implemented in practice in situations with a large number of alternatives. An example of this is in Aoki and Shirai (2000), in which there are as many value functions as there are employed agents in the model.
In this case, they could just use the value function for the mean. See also Chapter 9, where this kind of approximation is used.With many alternatives, the expressions for the value functions involve sums of many terms on the right-hand side. We discuss two aspects of value-function evaluations in such context. First, we discuss how the value functions discussed in the preceding section may be obtained under some circumstances. Then, we point out an interesting connection with the extreme values in evaluations of value functions consisting of many alternative returns. This connection is helpful in value-function evaluations.
6.5