Dynamic focus programming: A new approach to sequential decision problems under uncertainty

A new approach to sequential decision problems under uncertainty named dynamic focus programming is proposed with the focus theory of choice. In dynamic focus programming, there are two distinct evaluation systems: Positive and negative ones. Each possible path consisting of a decision sequence from the initial stage to the final stage and the associated states is examined. In the positive evaluation system, for each decision in the initial stage, if a path starting from it can bring about a relatively low total cost with a relatively high probability, then this path is selected as the positive focus path of this decision; based on the positive focus paths of all initial decisions, a decision maker chooses a most-preferred decision rule. In the negative evaluation system, for each decision in the initial stage, if a path starting from it can bring about a relatively high total cost with a relatively high probability, then this path is selected as the negative focus path of this decision; based on the negative focus paths of all initial decisions, a decision maker chooses a most acceptable decision rule. For a specific sequential decision problem, only one system is activated; as for which one works, it is strongly dependent on decision maker's personality and the framing. We apply dynamic focus programming to a real bidding decision-making problem: We obtain the optimal decision rule and gain the behavioral insights of the decision maker.