There are many texts on strategy and competition in a variety of contexts. However, there is a concept I feel is not well understood and certainly not well stated – building the massively complex and varying decision tree/optimal play from fairly generic components that humans like us can understand. This approach allows you to estimate work effort more precisely and to re-use the lessons you’ve learned in various life contexts to new situations.
The decomposition is: work functions (with probability adjustments) -> decision point (rock-paper-scissors), possibly with stochastic outcome -> feedback/decay -> repeat.
You next will read, in order:
- The underpinnings of why this is a good approximation in a wide variety of situations
- An example of how this breaks down complexity
- A discussion outlining how this generalizes to other situations. (The page “Notes on Types of Games and the Ideal Gaming Experience” on this site briefly reiterates these concepts in the context of amusement games.)
This decomposition is valid because real-life strategies typically occur in the context of:
– Large amounts of repetition, possibly infinite. Although individual strategists come and go (an individual strategist could be exploited), the situations they encounter recur at high enough frequency to draw general conclusions, so that non-repeated games are the uncommon case.
– Imperfect information is limited to well known categories such as physical impossibility of prediction (weather) and human’s internal intent (e.g. rock-paper-scissors), subject to a relatively small cost function for acquiring more accurate information. In some real-life situations, such as living in North Korea, gaining information often does have an infeasible cost; however, in those situations, and in many vaguely similar ones (e.g. Russia, the PRC), the value-maximizing response is easy to determine: kill all the enemies until the situation improves.
– Cooperation and signaling are difficult to prevent.
I do not think that the mainstream literature of game theory is far-off in a computational sense; however, most of the simplifications you see are inapplicable/suboptimal under the above conditions.
As exposition, I re-introduce some of the concrete concepts in question:
RPS/Janken: strategy that involves choosing a hard counter or dominant strategy to the choice you anticipate your opponent will select.
Game theoretics with perfect information: the science of deriving the optimal response to a certain opposing choice.
Prediction under uncertainty: the art of bounding and modeling probability functions that represent a future reality.
Economic investment: building up resources that can provide advantages in competition.
Training: building human competency in simulated scenarios that at least partially represent the competitive context.
Experience: actually doing the activity in question, and likely gaining competence or information in the process.
Competence: actually doing/being able to do what you were told/believe is the correct response.
Feedback loop: adjusting the above concepts in light of the results of competitive situation X, to gain advantage in competition X+1. Since I am assuming this is a concept in the following discussion, I also assume that the competitors know that there will be a series of competitive situations, if applicable to the problem.
Volatility: the level of variation in results based on either truly random phenomena, and phenomena that are difficult to precisely measure.
May also refer to the situation where a particular strategic approach can result in more widely varying outcomes than another strategic approach.
Concept Relationship Introduction: Light Firearm Infantry Situation
As a first approximation to the breadth of the situation, let us consider
the situation of military infantry armies, armed with the early
20th-century firearms. The military strategist typically wishes to
identify either the point of most effective attrition, or else to find the
most suitable point for a breakthrough, in order to gain decisive advantage
over the enemy army. The strategist’s initial (non-RPS problem) is simple:
rank the enemy forces’ combat effectiveness (fewest/weakest/least-well-supplied/most
isolated/non-reinforceable troops), then move all available forces to that
point for the attack, trap, or other initiation of combat operations. To
perform this task, he requires intelligence merely on the enemy’s force
disposition; if he has perfect information about the enemy forces, there is no RPS,
no prediction under uncertainty, no economic investment and other factors because
of the limited time scope of a single battle. The strategist may know at this
point that his troops cannot win the battle.
This initial subsection of the military strategy problem assumes that the
movement of troops is effectively instantaneous, and that the enemy does not
have the capability of reacting to those movements, or taking some other
action that changes the force dispositions. This is where we begin to consider
that ourselves and our enemy have varying outcomes based on choices made in
roughly discrete sections of time to which we cannot immediately react – in other
words, the RPS element. If we could instantly see the opposing force’s moves
and adjust our own forces, we would immediately restore maximum achievable combat
advantage. Nor would RPS matter if the enemy’s movements did not change the
most optimal point of attack. The amount of time, and the imperfection of
information about the enemy disposition, determine the importance of correct
RPS play.
Once we have an RPS element, the Markov-chain/Monte Carlo-type game theoretics
come into play. That is, the two sides do not merely consider the next move,
but consider the chain of moves, as well as such a chain can be estimated. In
blocking move-zone strategy games such as chess or Go, such chains can be
horrifically complicated. However, in the military situations, the chain tends
to be more tractable due to various practical considerations such as additive
advantage, i.e. the various military advantages, such as troop strength and
position, are rarely relatively decreased (compared to the opponent’s) by a
significant victory. In such a situation, the two parties will use approaches
that identify clusters of highly advantageous positions within the chain of moves.
Once we establish the general competitive situation, and what moves will
result in which victory for either side, according to the actual
dispositions of forces, we then add information to our decision by using
prediction under uncertainty to concretize or substitute probability functions
for true unknowns. At this point, we can estimate the best next move, which
may be simply to gather more information about the opponent. Our value
judgment about the next best move may not simply be about the highest average
expectation, but may also incorporate threshold requirements – in other words,
the strategic approach may maximize value by making choices which lower
volatility of results.
Normally we consider this as the “tactical” or “operational” approach, where
the availability of resources to execute a military action are assumed fixed
due to a limited time constraint. If we then remove that time constraint, to
consider other factors such as economic investment and training, then we see
that in subsequent time intervals, the RPS and chains of moves will vary in
time, so that it may make sense to defer or accelerate action if the cost of
waiting is relatively low or high. In a military context, typically the terms
“strategic” and “grand strategic” are used for the extended time horizon and
when larger political axes/objectives/values are incorporated into the game
theory.
At this point, the strategist’s job is finished; now the troops build skill
through training and experience, and they go to battle, showing how competent
they are in carrying out the orders. If the army is still intact after
battles, the strategist may be able to more accurately predict all of the
intellectual variables under uncertainty, and change choices according to that
new knowledge.
Re-Analyzing Competitive Situations
With some more thought, we can categorize the elements of the above complicated exposition:
Work functions: Intelligence gathering, calculation of force effectiveness,
Markov chain/Monte Carlo/field theory workouts, computation of each side’s
reactions to each enemy disposition (therefore to the computation of the
basic strategy), troop training and experience, strategist accuracy in
carrying out the computation tasks.
Decision point: Choosing the places and forces with which to attack.
This is dictated by the type and location of enemy’s forces, and any other
characteristics about your own forces, such as decayed morale, that you
don’t know when making the decision. It also is dictated by command lag
and reaction time of your own forces and those of the enemy. Both of these
factors can be reduced or eliminated by the above work functions. You
pick one of the ones that seem most optimal and hope that your opponent
isn’t lucky, or outplaying you somehow (e.g. by a spy in your camp).
Feedback/decay: The incorporation of knowledge about enemy troops,
enemy intelligence about your own troops, and the behavior of the opposing
commanders become inputs to your future work functions. Also, what the
enemy learned from this battle becomes an input to those future work
functions.
In other words, if you are economically superior and work your butt off,
in the military example, the enemy has no chance to stop what you are doing.
The enemy would require weapons of mass destruction to break even with you.
We can go further: if the enemy has a predictable strategy, there is no RPS
element at all and the matter of defeating the enemy is simply outworking
him and having more skill and resources when it counts.
How This Applies To The Elements of Strategy
Work Functions:
Game theoretics with perfect information
Prediction under uncertainty
Economic investment
Training
Competence
Decision Point:
RPS/Janken
Application of the game theoretics to apply probabilities to each choice
Feedback/Decay:
Experience
Other Applications
Business competition is usually about work functions. Although reading the Harvard Business Review might lead you to believe that competition is all about business strategy, it takes billions of dollars of work functions even to approach the point of being in a game where the competitors can meaningfully hide information from you, as their choice vs. yours.
While there is a tremendous amount of uncertainty in certain business R&D, exploration, and especially demand function decisions, those are not choices against your competitors: they are the reality of advanced physics and science, which is hard to discover; the capability of your people, which is uncertain given the unknown reality and your own limited understanding of your own people; and the metaphysically intractable problem of determining general human reactions and sentiments.
Proper civil government is not even a matter of decision points at a macro level. It is all work functions and feedback: understanding the history of the situation (looking at the experience of others and feeding that back), and working to implement the justice system, the economic management and environmental protection, and the welfare systems and civil engineering using the processes that, using your historical and scientific knowledge, are best suited to the situation.