(In the paper, the term "picul" is copied from the English version 
I used for the entire paper. As I understand the term "picul" was used as unit 
measuring grain in China during Sun Tzu era.)



I. INTRODUCTION

        Sun Tzu wrote his Strategy in about 300 B.C. Since then
the Strategy has influenced both Eastern and Western warfare. Nowadays, Sun
Tzu's Strategy is taught in military schools around the world. In the last few
years, there has even been rush to study and apply the concepts of Sun Tzu's
Strategy in business in Southeast Asia.


II. ABOUT SUN TZU'S STRATEGY

A. Central Idea
        The Strategy's main idea is to use marginal cost and benefit analysis,
information cost, and expectation to achieve allocation efficiency.

B.
Methodology
        There is no data to support the Strategy itself. The data mentioned
in the Strategy was used to explain the concept more easily. The numbers in the 
Strategy provided an idea about the cost of a war, and some simple calculation
of ratios between armies.
        It is not wise to read the Strategy by its face
meaning in Chinese. Since every phase has its own unique meaning. That is why
the Strategy has the feasibility  to be applied to different situations with
fast changing factors.

C. Title
        There is no standard English for Sun Tzu's thirteen prinsiples. In this 
paper, I refer to  it as "The Strategy" or "Strategy".


III. MODELING

A. Seven Factors of Victory
        Sun Tzu believed that the seven factors: moral reasons for
fighting a war, generals' ability, weather and geographical conditions, discipline of 
army, quality of army, education and training of troops, and clearance of the rules can be 
quantified and formulated into a calculated model which can determine which army could win a battle.

B. Calculated Modeling and Victory
        Sun Tzu wrote, "Now the general who wins a battle makes many calculations in his temple where 
the battle is fought. The general who lose a battle but few calculations beforehand. Thus do many 
calculations lead to victory, and few calculations to defeat: how much more no calculation at
all! It is by attention to this point that I can foresee who is likely to win or lose".
        Sun Tzu directly stated that there is a positive relationship between
the number of calculations conducted by the general staff and their chance to
win on the battle field. As more calculations are carried out by the general
staff, they will know more about the relationship among their resources. This
knowledge will facilitate a better allocation of resources and as a result there
will be higher fighting efficiency.

C. Multi-dimensional Possible Production Frontier
        As general staffs try to figure out different combinations using their
resources to fight a war, they are actually doing a mapping of multi-dimensional
possible production frontier. When considering shifting resources from one
sector to another, general staffs are doing a marginal analysis on applying
resources in different fields.
        Sun Tzu did not state this important tactic out
because he believed that wars only happen in the short-run, as no country can
survive with a long war and the purpose of war is to use a minimum amount of
resources to solve conflict among countries. In the short-run situation, there
are many factors that could not be substituted, and it does not make much sense
for Sun Tzu to invent a demand curve to explain the marginal substitute rates
among non-existing substitute resources. 
        As Sun Tzu added more factors in his war game model, the pictures 
look more complicated and more closer to reality.
In a multi-dimensional model with factors that cannot be totally substituted
among each other, change in one factor will shift the entire function, and maybe
bring up a totally new picture in the war game model. Indeed, Sun Tzu pointed
out that the more practical and realistic way to utilize resources is by
studying the relationship among factors in the war game model. When general
staffs do calculations in their battle field models, marginal cost and benefit
analysis is carried out. They try to maximize their resources for productivity
(fighting ability within their constraints).

D. Middle Way and Pareto Condition
It is so easy for Chinese to understand the business cycle, since the concept of
cycle actually is imbedded in Chinese culture. As Confucius pointed out that the
best is not existing in the extremes, but in the middle. For anything, Confucius
believed that people should not go for too few or too much. We do not need to go
any further after reaching the best we can reach. There is always a best
combination existing, and Sun Tzu believed that the only way to find out the
best combination is by doing more calculation in modeling.

E. Tao of War
        Sun Tzu believed that there was no such universal way to fight and win every war,
since it always involved so many factors in the battle field and the changes in
every factor are so frequent. Furthermore, no two battles are the same. 
        We can view Sun Tzu's Strategy as a collection of a function. However, there will not
be any absolute answer from the function, since the variables used in the
function depend on the situation, plus the values of the variables will vary
from person to person. That is also the reason for its feasibility.
        The main idea of Sun Tzu on war is calculating the changes of factors which would influence 
the battle field situation. We can summarized Sun Tzu's idea on that by
the first sentence from Tao Tau King.  The Tao that can be told is not the eternal Tao.


IV. BASIC ECONOMIC CONCEPTS

A. Opportunity Cost
        Sun Tzu believed that war was a means to solve conflict, but not the best way to do it. War is
not created for its own sake. War is the opportunity cost of failure in
diplomacy between countries.
        Sun Tzu wrote, "In the practical art of war, the
best thing of all is to take the enemy's country whole and intact; to shatter
and destroy it is not so good. So, too, it is better to recapture an army entire
than to destroy it, to capture a regiment, a detachment or a company entire than
to destroy them. Hence to fight and conquer in all your battles is not supreme e
xcellence; supreme excellence consists in breaking the enemy's resistance
without fighting".

B. Cost and Benefit Analysis
        Sun Tzu wrote, "It is only one who is thoroughly acquainted with the evils of war that can thoroughly
understand the profitable way of carrying it on". Here, it simply shows that Sun
Tzu used the cost and benefit analysis as a standard rule for decision making.

C. Economy of Scale   
        Sun Tzu also mastered the technique of economy of scale
in fighting. As one has absolute advantage in terms of troops, he can avoid the
cost of direct fighting. Sun Tzu wrote, "It is the rule in war, if our forces
are ten to the enemy's one, to surround him; if five to one, to attack him; if
twice as numerous, to divide our army into two".


V. MARKET EQUILIBRIUM

Shortage and Increasing Prices
        In Sun Tzu's era, people knew about the relationship
between demand, supply, and price. As Sun Tzu recognized that there would be a
price increase for goods under shortage conditions. Sun Tzu wrote, "On the other
hand, the proximity of an army causes prices to go up; and high prices cause the
people's substance to be drained away".


VI. PRODUCTIVITY

A. Time and Productivity
        Sun Tzu wrote, "When you engage in actual fighting, if victory is
long in coming, then men's weapons will grow dull and their ardor will be
damped. If you lay siege to a town, you will exhaust your strength. Again, if
the campaign is protracted, the resources of the State will not be equal to the
strain". 
        Sun Tzu pointed out that the productivity of the troops and the costs
of war increase as a war is prolonged. Time was seem as a vital resource by Sun Tzu.

B. Innovation and Productivity
        As Sun Tzu recognized that a nation's physical resources for war 
were limited, he concluded that, only by using
creative general staffs could more different ways to utilize resources more
efficiently come out. Sun Tzu pointed out that creativity is unlimited.
        Sun Tzu wrote, "In all fighting, the direct method may be used for joining battle, but
indirect methods will be needed in order to secure victory. Indirect tactics,
efficiently applied, are inexhaustible as Heaven and Earth, unending as the flow
of rivers, and streams; like the sun and moon, they end but to begin anew; like
the four seasons, they pass away to return once more".
        In today's words, Sun Tzu understood the importance of how creativity can 
improve productivity by new methods of production and new technology.

C. Human Resources and Productivity
        Sun Tzu claimed that the ability of the general staff and the quality,
training, and education of the army are two of the seven basic factors to tell
which army can win on the battle field. Later, Sun Tzu also mentioned how
quickly physical resources will be used up once a war is started, but creativity
which benefits productivity is unlimited by any physical constraints and does
not have a diminishing return. Sun Tzu had insight on the importance of
investment in human capital and its return in terms of productivity.


VII. COST

A. Logistical Cost
        Sun Tzu understood that there is a positive relationship
between the distance of the battle field and the home country. This refers to
the transportation cost to support an army in a foreign country and its
communication lines. Sun Tzu wrote," Poverty of the State exchequer causes an
army to be maintained by contributions from a distance. Contributing to maintain
an army at a distance causes the people to be impoverished".

B. Localization and Logistical Cost
        In order to lower war expenses for battles on foreign land, Sun
Tzu stated that by utilizing foreign resources, one can reduce the expenses of
the army and its huge communication lines. Sun Tzu wrote, "Bring war material
with you from home, but forage on the enemy. Thus the army will have food enough
for its needs. ... Hence a wise general makes a point of foraging on the enemy.
One carload of the enemy's provisions is equivalent to twenty of one's own, and
likewise a single picul of his provender is equivalent to twenty from one's own store".

VIII. OTHER FUNCTIONS

A. Support from the Home Front

        Sun Tzu wrote, "The skillful soldier does not raise a second levy, neither are his
supply-wagons loaded more than twice". Here, Sun Tzu set a time limit on war and
a limit of financial responsibility for the nation, since Sun Tzu was concerned
with domestic living standards and the support from the home front in war; domes
tic support has a strong influence on the troop's fighting ability in Sun Tzu's model.

B. Psychological Warfare
        Sun Tzu set no constraints on how to win a war
or defeat an enemy. He also encourages the use of all different means to put one
in the advantage position. Psychological warfare is one of the ways to lower
enemy's ability with no direct contact.
        Sun Tzu wrote, "If your opponent is of
choleric temper, seek to irritate him. Pretend to be weak, that he may grow
arrogant. If he is taking his ease, give him no rest. If his forces are united,
separated them". There is nothing new to using psychological warfare to attack
the other side in a war. But if we find out that the relationship between an
enemy's ability and their expectations and values, we can relatively use lesser
resources to damage the enemy's fighting ability. If the marginal return of such
warfare is higher than the average return from other means, more resources will
be allocated to that use. As a result, the marginal return of resources in every
field are about the same, since it is not always possible to transfer resources
among different fields in a short-run period.

C. Spying

1. The Spying Function
In the usual situation, countries will try to spy for their enemies'
intelligence. As the social, cultural, and geographical constraints exist,
spying activities are always operated within the boundaries of constraint
factors. In order to maximize the utility of spying activities, every country
will push their spying activities to limits.
        We can see intelligence collection as a function of the resources spent on it. When a 
nation tries to maximize its intelligence collection, it will put the function of intelligence 
in the neighborhood of its constraint boundaries.

2. Crossing the Boundary, Enemy's expectation, and Change of Boundary
        One of the ways of spying suggested by Sun Tzu is conducting the spying activities 
out of the normal expected boundary.  Assuming the enemy side expects rational behavior on our 
side, the out of boundary operation will cause the enemy to change their expectations and 
as a result change the constraints of spying for our side.


IX. INFORMATION COST, ALLOCATION OF RESOURCES AND PRODUCTIVITY

        Sun Tzu wrote, "All warfare is based on deception. Hence, when able 
to attack, we must seem unable; when using our
forces, we must seem inactive; when we are near, we must make the enemy believe
we are far away; when far away, we must make him believe we are near." 
Here, Sun Tzu pointed out that by misinforming the enemy, one can enhance one's
productivity. As the enemy is fed with wrong information about the movement of
our troops, the enemy cannot allocate its resources at the most efficient level
to prevent our attacks. In other words, it enhances our side's productivity.
One of the famous quotes from Sun Tzu's strategy, "Attack him where he is
unprepared, appear where you are not expected", can be a good summary of this
idea. As the enemy is not expecting us to attack, they will not allocate enough
resources to defense, this will give a ratio advantage to our side, and boost up
the productivity of our troops in the battle field. 


X. SHORT-TERM GAINS AGAINST LONG-TERM GAINS

        Generally speaking, every side on the battle field tries to win
every battle, big and small, with minimum cost, and every battle is fought with
resources used efficiently: it will bring the final victory to the most
efficient side. 
        From Sun Tzu's point of view, it is not necessarily true. Sun
Tzu always emphasized the importance of the entire war game picture, rather than
a regional one. Troops can be easily trapped by the enemy by following small
scale planned victories. 
        Sun Tzu wrote, "Hold out baits to entice the enemy".
Short-term interests does not necessary reflect its true value in the long run.
The United States ground force used small units to attract North Vietnamese
regular divisions into showing themselves during the Vietnam war is an example
of using a short-term loss to make North Vietnamese pay greater cost. 


XI.
INVESTMENT PATTERN
        As Confucius said, "If you want to get your job well done,
you need to get your tools well-prepared first". Sun Tzu's Strategy gives its
reader an idea of how to project a long term strategy or to picture in their
mind the allocation of resources in the micro-level and highlight there
importance. This may be a precursor of the investment patterns of Korea, Japan,
and Taiwan in education, transportation infrastructure, and industrial research
and development. 
        Under evolutionary influences represented in the work of of
Confucius and Sun Tzu, Chinese, Korean, and Japanese have a totally different
mind set compared to the British, and Americans. Asians, under influences
represented in Confucius, are more likely to invest in the long-term and do not
appreciate any short-term profits, which are at the expense of their long-term
investment. Since Asians seem to invest just like the war game model projected
by Sun Tzu, their behavior is targeting long term results, but not a short run
local victory.


XII. HISTORICAL EXAMPLES OF APPLYING SUN TZU'S STRATEGY

A.
Mongolian
        Mongolians used speed and low information cost to enhance its army's
fighting ability in it Asia-Europe campaign. In order to maintain the speed and
keep the war expense low, Mongolians tried to utilize resources captured in the
field, both human and physical, to finance the next coming campaign. This d
irectly solved the cost and distance problems of communication lines from home
and kept the Mongolian war machine running for forty-five years.

B. Japan's attack on Pearl Harbor
        The Japanese Imperial Navy attacked the
United States Navy at Pearl Harbor, Hawaii, in 1941, using a gap in information
to trade for fighting ability against their stronger American counterpart.

C.
North Vietnamese in Vietnam War
        During the Vietnam War, the South Vietnamese
government had absolute advantages in terms of military power to defend itself
from the attacks of North Vietnam. Wu Chi-Ming, head of North Vietnam,
recognized that there was no way to confront the South Vietnamese and American
ground forces in terms of modern warfare. Wu then used time, morale, geographic
condition, and human life, to trade for its disadvantage in firepower. This
prolonged the war and caused the American troops to withdraw from Vietnam under
the pressure of high costs.


XIII. CONCLUSION

        This paper only discusses part of Sun Tzu's Strategy, but it covers the major ideas 
of Sun Tzu. It is easy to discover that Sun Tzu was acting as an economic man in his time. 
He tried to maximum his utility within constraints, which included limited physical
resources and environmental conditions. Sun Tzu paid attention to details on the
micro level and at the same time was targeted resources for long term goals. 
By efficiently allocating resources and lowering information cost, Sun Tzu tried
to put every bit of resource to its best use. 
        Sun Tzu's Strategy can be divided into five different levels.
First Level: 
Achieving allocation efficiency by understanding the relationship of different production factors.
Second Level:
Apply the mathematical modeling technique to analyze the production function of
the enemy. Then refine our plan to achieve higher efficiency by analyzing both
ours and enemy's production function sets.
Third Level: 
By doing more research, we can find a breakthrough in productivity. 
Forth Level: 
New methods in lowering information cost can enhance productivity and at the same time increase
the enemy's cost.
Fifth Level: 
By feeding incorrect information to enemy, we can
lead the enemy to actively allocate its resources inefficiently. 
        Without any ideological constraints, Sun Tzu tried to map the possible production frontier
and find out the most efficient way of production.




APPENDIX NOTES ON THE TRANSLATION
        Sun Tzu's Strategy has been widely translated, and the translations
generally reflect the cultural or religious background of the translators. Since
the time of the Tang Dynasty (A.D. 618 to 906) continuing through to the
present, Sun Tzu's work was known and studied in Japan. It was not introduced
into the West until 1772 when the French Jesuit Fr. P. Amiot translated it from
Chinese into French. It has been said that this version was a favorite of
Napoleon. Translations of Sun Tzu began to appear in Russia as early as the
1800s, the most notable a 1950 translation by N. Konrad.
        In 1905, British Army Capt. E. F. Calthrop translated The Art of Strategy into English from a Japanese
translation. It was soon after translated directly from Chinese into English by
Lionel Giles, curator of Oriental Books and manuscripts at the British Museum.
The Giles translation, entitled The Art of War, was published in 1910 and has
remained in print ever since, most recently reissued in a 1983 edition with
commentary in German by von Bruno Navarra, while in 1956 the Soviet military
published a Chinese-to-Russian translation by Lt. J. I. Siderenko. An American
translation by retired U.S. Marine Brig. Gen. Samuel B. Griffith, entitled The
Art of War, was published in 1963. 
        This paper is using the version in 1910 by Lionel Giles.