MMP.8.SD:1 - Problem frame

Use this when a choice changes what can be done or learned later, and comparing its immediate result does not settle the useful course of action. You might reserve a resource for a later request, inspect an unfamiliar document before choosing how to process it, or pursue a target whose attainment depends on several moves.

Start with two possible first actions. For each, write what becomes available before the next choice and what the next choice can change. This small decision tree often reveals the missing resource, remembered event or uncertainty that a proposed “current state” has discarded.

The object being constructed is a sequential decision model: a mathematical account connecting available information, allowed actions, subsequent observations and accumulated consequences. Its result lets a reader compare a present action together with an admissible continuation. A continuation is the later policy: a rule for choosing actions from the information available then.

This is the sequential refinement of MMP.8 - Formulate Information-Dependent Choices Mathematically. It retains that pattern’s separation of chosen quantities, uncontrolled circumstances and information available at each choice. It adds the construction of a state sufficient for the selected decision problem and the relation between current action and remaining consequence. A short history tree is a valid starting model; a compact state becomes useful when the tree repeats questions or grows too large.

A reader can work the finite cases with conditional probability, finite sums and maxima, or with sets of possible outcomes. For continuous, constrained or indefinitely continuing models, the person supplying the mathematical argument needs the relevant preparation in stochastic control, decision theory or the applicable field. This can be the reader or an available specialist. Give a specialist the actual timing, allowable actions and consequence criterion; ask for the resulting model and its limitations.

Not this pattern when the useful comparison is already a single choice with no consequential continuation. Use MMP.8 directly. If the decision model is adequate and only its solution is expensive, the next work is computational. If the difficulty is deciding whose interests or which consequences should count, obtain that choice from the responsible people and the applicable decision or strategy practice.