Strategy
And The State Framework

**I. Introduction**

One of the most powerful concepts for strategy development is
that of a state. It is vastly more efficient than decision trees
and more complete than *ad hoc* strategy diagrams. The state
completely describes the relevant aspects of a strategy situation.
At any one time, it summarizes the information about past actions,
events, and observations required for immediate decision making.
Over a time horizon, the state framework provides the structure
required for design of strategy.

Pictorially, the state evolves step-by-step (or stage-by-stage)
as in the figure at the top of the next page. The state at any one
stage is influenced by the state

at the previous stage and by actions, events, and observations at
the current stage. This process continues stage-by-stage. There is
a fixed formula for how these influences translate directly into
new state values or probabilistically affect the state.

Example. (Development Effort) Consider a company developing a
new product variation. The issue is how much financial resource
should be allocated during each six-month period. Investing heavily
leads to fast time to market and hence higher revenue, but also to
less efficient use of resources and hence additional cost relative
to a conservative approach. What is the best rate of
development?

We suppose that progress advances by 0%, 20%, 40%, or 60% each
period, corresponding to whether $0, $1 million, $3 million, or $7
million is allocated that period. If the product is completed in 2,
3, 4, or 5 periods, the total discounted net revenue obtained from
the product is expected to be, correspondingly, 10, 9, 7, or 4
millions of dollars.

The situation can be described by a single state variable at
each period, denoting development progress and a single action
variable corresponding to the amount invested that period. The
single state variable has the 6 potential values 0, 20, 40, 60, 80,
and 100, all being percentages of completion.

**II. Defining States**

Typically, state variables can be classified according to six
types:

1. Internal progress variables.
These variables describe project progress (for example, a percent
of product development or an estimate of the quality of the final
product).

2. Resource status variables.
These variables define the physical and human resources available
to the firm. These variables also define actions that must be
carried forward as directly affecting

future times. For example, in designing an oil field extraction
plan, an early decision to drill at site A instead of site B must
be carried along as a state variable to all future phases.

3. Market variables. These
variables describe the market in which the company must operate.
They may be current market prices or estimates of future market
prices.

4. Competitive variables. These
variables describe the status of competition.

5. Regulation and standards
variables. These variables describe the status of possible
government action (such as tax policy or environmental
requirements) or industry standards.

6. Financial variables. Often
only total discounted cash flow is required and hence no state is
needed. In cases where there is a financial constraint, a state
variable keeps track of the constraint.

In most applications the state will not include variables for
all of these categories. Good analysis involves the selection of a
few variables that are critical to strategy design. When first
approaching a strategy creation situation, however, both the novice
and the expert strategy designer may usefully define perhaps a
dozen state variables. Through intuition, experience, and detailed
probing this number can usually be reduced to about a
half-dozen.

Considerations of computational ease dictate that most state
variables are allowed to take on only a small number of possible
values. Some variables, such as "research success or failure," will
have only two possible values. Others, such as, "product quality
being high, medium, or low" take on a small number. Some variables,
such as "market price," may have many potential values.

**III. Influence Variables**
The influence variables are the actions, events, and
observations that effect the state variables at the current
stage.

1. Actions. As a general rule
actions are controlled by the entity carrying out the strategy.
Actions are a consequence of decisions. Typically, actions depend
on the most recent state and the current values of other influence
variables. Examples of action include deployment of resources,
gathering of information, delay or termination of the project, or
major change of project direction.

2. Events. Events are those
factors that cannot be controlled, and are most often treated as
random. Examples include market prices or expectations of future
market prices, government actions, standards, competitor actions,
and physical outcomes (such as machine breakdowns or research
successes).

3. Observations. Observations
are often interchangeable with events. The difference is that the
(unknown) result of the observation is not available without
conscious effort. Examples are test results in oil exploration,
results of market surveys, and test market results.

State variables and influence variables often have similar
names. For example, market price is a state and also an influence.
The difference is that the (state) market price from the previous
period as well as a current price change (influence) determines the
current market price (state). Thus influences are often incremental
while states are absolute.

**IV. Computational Ease**

Overall computational difficulty is proportional to the product
P of the numbers of possible values of all of the state variables.
That is, it is the number of all combinations of state values.
Hence if there are six variables and the number of possible values
are 100, 10, 2, 3, 10, 2, respectively, then *P* = 100 x 10 x
2 x 3 x 10 x 2 = 120,000. A *P* of this order means that the
problem is fairly complex, but not unreasonably so.

By contrast, the number of final nodes in a decision tree
usually grows geometrically as *K*^{n} where *n*
is the number of stages. The quantity *K* depends on the
number of action, event, and status combinations, and hence even
modest strategy problems have millions or hundreds of millions of
final nodes. Often the number *K* is about equal to the number
of state combinations *P*. Hence the number of final nodes in
a 5 stage tree with the same *K* as in the previous paragraph
would be 120,000^{5} which is over 2 x 10^{25}, or
billions of times larger than the number of grains of sand on
Earth.

**V. Results**

Once constructed, the state system can be used to find an
optimal strategy and display various aspects of any given strategy.
Typically, an important criterion is a measure of financial value.
Here all the concepts and techniques of Investment Science, as
represented for example in this Newsletter series, are applicable.
For example, private uncertainties will be discounted at the
risk-free rate, and market uncertainties at the growth rate of the
market.

In addition, various statistics, sensitivities, and special
valuations can be displayed. Here is a list of possible uses.

**1. Strategy evaluation.**

This is perhaps the most useful application in practical
situations. The strategy team suggests strategies that are
operationally feasible and these are evaluated according to many
criteria. Often, excellent strategies are obtained this way,
together with a good intuitive understanding of the advantages and
disadvantages of various contending strategies.

2. Optimization.

Given a particular criterion, such as total discounted cash flow,
the optimal strategy can be computed using dynamic programming.
This strategy can then be simplified if necessary to produce an
operationally feasible policy.

3. Sensitivity.

The sensitivity of various measures to variations in some of the
parameters of the model can be computed and displayed.

4. Scenario evaluation.

A scenario is a predetermined sequence of some of the state
variables or of the events and observations.

For example, one might project a rate of price decrease after a
product is introduced, rather than allowing the price sequence to
be random. This type of analysis can show how robust a particular
strategy is to scenarios of concern.

5. Scenario averaging.

As a short cut to a full probabilistic model of uncertainties,
where say a price changes randomly from period to period, one may
define a small set of typical scenarios and then evaluate
strategies against an average of these scenarios. That is, the
scenarios are assigned probabilities and the single strategy is
evaluated according to its average performance against these. This
approach is most valuable when the most critical element of a
strategy is the current action (or decision).

There are variations of these themes. A good state model
combined with various methods of analysis and optimization can
produce excellent strategies together with intuitive rationales for
their benefits. Investment Science concepts are essential to
providing the correct strategy performance measures.

As a simple exercise, you may wish to find the optimal solution
to the example given in the early part of this article. One way to
do it is to use dynamic programming. At first, assume that the
appropriate discount rate is 0%. Then see what happens if the
discount rate is positive. A solution will be posted on the website
next month.