Economic adaptive decision processes

A sequential adaptive economic decision process can generally be broken down into three interrelated sequential processes. The first is a stochastic environmental process; the second is a historical process which generates a record of the past environmental events; and the third is the decision process itself. Many different kinds of historical processes are possible. Heuristic processes are briefly considered but this paper is mainly concerned with the Bayesian process. Assuming a beta a priori probability function a maximum liklihood estimate function or subjective probability function can be developed for the decision maker\´s use. A decision process generally implies that the decision maker will display some optimal behavior pattern. It will be assumed that the decision maker seeks to maximize the rate of growth of his personal resources. This assumption leads to the formulation of the sequential adaptive process as a dynamic programming problem. The solution of the dynamic programming problem leads to an optimal policy for the decision maker which is the "best" he can do with only limited information about his environmental process. As time passes the optimal policy improves and approaches, in the probability limit, the "best" that can be done having full information about the environmental process. The expected rate of growth of the decision maker\´s resources is a function of his subjective view of the entropy of the environment and as time passes this expected rate of growth approaches, in the probability limit, a function of the actual entropy of the environment.